%!PS-Adobe-3.0 %%Title: (Microsoft Word - machinelearn3) %%Creator: (Microsoft Word: LaserWriter 8 8.3.4) %%CreationDate: (10:32 PM Tuesday, March 25, 1997) %%For: (peter) %%Pages: 8 %%DocumentFonts: Times-Bold Times-Roman Times-Italic Times-BoldItalic Symbol TimesNewRomanPS-BoldMT TimesNewRomanPS-BoldItalicMT %%DocumentNeededFonts: Times-Bold Times-Roman Times-Italic Times-BoldItalic Symbol TimesNewRomanPS-BoldMT TimesNewRomanPS-BoldItalicMT %%DocumentSuppliedFonts: %%DocumentData: Clean7Bit %%PageOrder: Ascend %%Orientation: Portrait %%DocumentMedia: Default 612 792 0 () () %ADO_ImageableArea: 31 31 583 761 %%EndComments userdict begin/dscInfo 5 dict dup begin /Title(Microsoft Word - machinelearn3)def /Creator(Microsoft Word: LaserWriter 8 8.3.4)def /CreationDate(10:32 PM Tuesday, March 25, 1997)def /For(peter)def /Pages 8 def end def end save /version23-manualfeedpatch where { pop false } { true }ifelse % we don't do an explicit 'get' since product and version MAY % be in systemdict or statusdict - this technique gets the lookup % without failure statusdict begin product (LaserWriter) eq % true if LaserWriter version cvr 23.0 eq % true if version 23 end and % only install this patch if both are true and % true only if patch is not installed and is for this printer % save object and boolean on stack dup { exch restore }if % either true OR saveobject false dup { /version23-manualfeedpatch true def /oldversion23-showpage /showpage load def /showpage % this showpage will wait extra time if manualfeed is true {% statusdict /manualfeed known {% manualfeed known in statusdict statusdict /manualfeed get {% if true then we loop for 5 seconds usertime 5000 add % target usertime { % loop dup usertime sub 0 lt { exit }if }loop pop % pop the usertime off the stac }if }if oldversion23-showpage }bind def }if not{ restore }if /md 228 dict def md begin/currentpacking where {pop /sc_oldpacking currentpacking def true setpacking}if %%BeginFile: adobe_psp_basic %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /bd{bind def}bind def /xdf{exch def}bd /xs{exch store}bd /ld{load def}bd /Z{0 def}bd /T/true /F/false /:L/lineto /lw/setlinewidth /:M/moveto /rl/rlineto /rm/rmoveto /:C/curveto /:T/translate /:K/closepath /:mf/makefont /gS/gsave /gR/grestore /np/newpath 14{ld}repeat /$m matrix def /av 83 def /por true def /normland false def /psb-nosave{}bd /pse-nosave{}bd /us Z /psb{/us save store}bd /pse{us restore}bd /level2 /languagelevel where { pop languagelevel 2 ge }{ false }ifelse def /featurecleanup { stopped cleartomark countdictstack exch sub dup 0 gt { {end}repeat }{ pop }ifelse }bd /noload Z /startnoload { {/noload save store}if }bd /endnoload { {noload restore}if }bd level2 startnoload /setjob { statusdict/jobname 3 -1 roll put }bd /setcopies { userdict/#copies 3 -1 roll put }bd level2 endnoload level2 not startnoload /setjob { 1 dict begin/JobName xdf currentdict end setuserparams }bd /setcopies { 1 dict begin/NumCopies xdf currentdict end setpagedevice }bd level2 not endnoload /pm Z /mT Z /sD Z /realshowpage Z /initializepage { /pm save store mT concat }bd /endp { pm restore showpage }def /$c/DeviceRGB def /rectclip where { pop/rC/rectclip ld }{ /rC { np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K clip np }bd }ifelse /rectfill where { pop/rF/rectfill ld }{ /rF { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl fill gR }bd }ifelse /rectstroke where { pop/rS/rectstroke ld }{ /rS { gS np 4 2 roll :M 1 index 0 rl 0 exch rl neg 0 rl :K stroke gR }bd }ifelse %%EndFile %%BeginFile: adobe_psp_colorspace_level1 %%Copyright: Copyright 1991-1993 Adobe Systems Incorporated. All Rights Reserved. /G/setgray ld /:F1/setgray ld /:F/setrgbcolor ld /:F4/setcmykcolor where { pop /setcmykcolor ld }{ { 3 { dup 3 -1 roll add dup 1 gt{pop 1}if 1 exch sub 4 1 roll }repeat pop setrgbcolor }bd }ifelse /:Fx { counttomark {0{G}0{:F}{:F4}} exch get exec pop }bd /:rg{/DeviceRGB :ss}bd /:sc{$cs :ss}bd /:dc{/$cs xdf}bd /:sgl{}def /:dr{}bd /:fCRD{pop}bd /:ckcs{}bd /:ss{/$c xdf}bd /$cs Z %%EndFile %%BeginFile: adobe_psp_uniform_graphics %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /@a { np :M 0 rl :L 0 exch rl 0 rl :L fill }bd /@b { np :M 0 rl 0 exch rl :L 0 rl 0 exch rl fill }bd /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /x1 Z /x2 Z /y1 Z /y2 Z /rad Z /@q { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct fill }bd /@s { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs np x2 x1 add 2 div y1 :M x2 y1 x2 y2 rad arct x2 y2 x1 y2 rad arct x1 y2 x1 y1 rad arct x1 y1 x2 y1 rad arct :K stroke }bd /@i { np 0 360 arc fill }bd /@j { gS np :T scale 0 0 .5 0 360 arc fill gR }bd /@e { np 0 360 arc :K stroke }bd /@f { np $m currentmatrix pop :T scale 0 0 .5 0 360 arc :K $m setmatrix stroke }bd /@k { gS np :T 0 0 :M 0 0 5 2 roll arc fill gR }bd /@l { gS np :T 0 0 :M scale 0 0 .5 5 -2 roll arc fill gR }bd /@m { np arc stroke }bd /@n { np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix stroke }bd %%EndFile %%BeginFile: adobe_psp_customps %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /$t Z /$p Z /$s Z /$o 1. def /2state? false def /ps Z level2 startnoload /pushcolor/currentrgbcolor ld /popcolor/setrgbcolor ld /setcmykcolor where { pop/currentcmykcolor where { pop/pushcolor/currentcmykcolor ld /popcolor/setcmykcolor ld }if }if level2 endnoload level2 not startnoload /pushcolor { currentcolorspace $c eq { currentcolor currentcolorspace true }{ currentcmykcolor false }ifelse }bd /popcolor { { setcolorspace setcolor }{ setcmykcolor }ifelse }bd level2 not endnoload /pushstatic { ps 2state? $o $t $p $s $cs }bd /popstatic { /$cs xs /$s xs /$p xs /$t xs /$o xs /2state? xs /ps xs }bd /pushgstate { save errordict/nocurrentpoint{pop 0 0}put currentpoint 3 -1 roll restore pushcolor currentlinewidth currentlinecap currentlinejoin currentdash exch aload length np clippath pathbbox $m currentmatrix aload pop }bd /popgstate { $m astore setmatrix 2 index sub exch 3 index sub exch rC array astore exch setdash setlinejoin setlinecap lw popcolor np :M }bd /bu { pushgstate gR pushgstate 2state? { gR pushgstate }if pushstatic pm restore mT concat }bd /bn { /pm save store popstatic popgstate gS popgstate 2state? { gS popgstate }if }bd /cpat{pop 64 div setgray 8{pop}repeat}bd %%EndFile %%BeginFile: adobe_psp_basic_text %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg true def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg false store }if pop }if }bd /$f[1 0 0 -1 0 0]def /:ff{$f :mf}bd /MacEncoding StandardEncoding 256 array copy def MacEncoding 39/quotesingle put MacEncoding 96/grave put /Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis/Udieresis/aacute /agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute/egrave /ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde/oacute /ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex/udieresis /dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/notequal/AE/Oslash /infinity/plusminus/lessequal/greaterequal/yen/mu/partialdiff/summation /product/pi/integral/ordfeminine/ordmasculine/Omega/ae/oslash /questiondown/exclamdown/logicalnot/radical/florin/approxequal/Delta/guillemotleft /guillemotright/ellipsis/space/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide/lozenge /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright/fi/fl /daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex/Idieresis/Igrave /Oacute/Ocircumflex/apple/Ograve/Uacute/Ucircumflex/Ugrave/dotlessi/circumflex/tilde /macron/breve/dotaccent/ring/cedilla/hungarumlaut/ogonek/caron MacEncoding 128 128 getinterval astore pop level2 startnoload /copyfontdict { findfont dup length dict begin { 1 index/FID ne{def}{pop pop}ifelse }forall }bd level2 endnoload level2 not startnoload /copyfontdict { findfont dup length dict copy begin }bd level2 not endnoload md/fontname known not{ /fontname/customfont def }if /Encoding Z /:mre { copyfontdict /Encoding MacEncoding def fontname currentdict end definefont :ff def }bd /:bsr { copyfontdict /Encoding Encoding 256 array copy def Encoding dup }bd /pd{put dup}bd /:esr { pop pop fontname currentdict end definefont :ff def }bd /scf { scalefont def }bd /scf-non { $m scale :mf setfont }bd /ps Z /fz{/ps xs}bd /sf/setfont ld /cF/currentfont ld /mbf { /makeblendedfont where { pop makeblendedfont /ABlend exch definefont }{ pop }ifelse def }def %%EndFile %%BeginFile: adobe_psp_derived_styles %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /wi version(23.0)eq { { gS 0 0 0 0 rC stringwidth gR }bind }{ /stringwidth load }ifelse def /$o 1. def /gl{$o G}bd /ms{:M S}bd /condensedmtx[.82 0 0 1 0 0]def /:mc { condensedmtx :mf def }bd /extendedmtx[1.18 0 0 1 0 0]def /:me { extendedmtx :mf def }bd /basefont Z /basefonto Z /dxa Z /dxb Z /dxc Z /dxd Z /dsdx2 Z /bfproc Z /:fbase { dup/FontType get 0 eq{ dup length dict begin dup{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall /FDepVector exch/FDepVector get[exch/:fbase load forall]def }/bfproc load ifelse /customfont currentdict end definefont }bd /:mo { /bfproc{ dup dup length 2 add dict begin { 1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse }forall /PaintType 2 def /StrokeWidth .012 0 FontMatrix idtransform pop def /customfont currentdict end definefont 8 dict begin /basefonto xdf /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin basefont setfont ( )dup 0 4 -1 roll put dup wi setcharwidth 0 0 :M gS gl dup show gR basefonto setfont show end }def }store :fbase }bd /:mso { /bfproc{ 7 dict begin /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxa 1 ps div def basefont setfont ( )dup 0 4 -1 roll put dup wi 1 index 0 ne { exch dxa add exch }if setcharwidth dup 0 0 ms dup dxa 0 ms dup dxa dxa ms dup 0 dxa ms gl dxa 2. div dup ms end end }def }store :fbase }bd /:ms { /bfproc{ dup dup length 2 add dict begin { 1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse }forall /PaintType 2 def /StrokeWidth .012 0 FontMatrix idtransform pop def /customfont currentdict end definefont 8 dict begin /basefonto xdf /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxb .05 def basefont setfont ( )dup 0 4 -1 roll put dup wi exch dup 0 ne { dxb add }if exch setcharwidth dup dxb .01 add 0 ms 0 dxb :T gS gl dup 0 0 ms gR basefonto setfont 0 0 ms end end }def }store :fbase }bd /:mss { /bfproc{ 7 dict begin /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxc 1 ps div def /dsdx2 .05 dxc 2 div add def basefont setfont ( )dup 0 4 -1 roll put dup wi exch dup 0 ne { dsdx2 add }if exch setcharwidth dup dsdx2 .01 add 0 ms 0 .05 dxc 2 div sub :T dup 0 0 ms dup dxc 0 ms dup dxc dxc ms dup 0 dxc ms gl dxc 2 div dup ms end end }def }store :fbase }bd /:msb { /bfproc{ 7 dict begin /basefont xdf /FontType 3 def /FontMatrix[1 0 0 1 0 0]def /FontBBox[0 0 1 1]def /Encoding StandardEncoding def /BuildChar { exch begin sD begin /dxd .03 def basefont setfont ( )dup 0 4 -1 roll put dup wi 1 index 0 ne { exch dxd add exch }if setcharwidth dup 0 0 ms dup dxd 0 ms dup dxd dxd ms 0 dxd ms end end }def }store :fbase }bd /italicmtx[1 0 -.212557 1 0 0]def /:mi { italicmtx :mf def }bd /:v { [exch dup/FontMatrix get exch dup/FontInfo known { /FontInfo get dup/UnderlinePosition known { dup/UnderlinePosition get 2 index 0 3 1 roll transform exch pop }{ .1 }ifelse 3 1 roll dup/UnderlineThickness known { /UnderlineThickness get exch 0 3 1 roll transform exch pop abs }{ pop pop .067 }ifelse }{ pop pop .1 .067 }ifelse ] }bd /$t Z /$p Z /$s Z /:p { aload pop 2 index mul/$t xs 1 index mul/$p xs .012 mul/$s xs }bd /:m {gS 0 $p rm $t lw 0 rl stroke gR }bd /:n { gS 0 $p rm $t lw 0 rl gS gl stroke gR strokepath $s lw /setstrokeadjust where{pop currentstrokeadjust true setstrokeadjust stroke setstrokeadjust }{ stroke }ifelse gR }bd /:o {gS 0 $p rm $t 2 div dup rm $t lw dup 0 rl stroke gR :n }bd %%EndFile /currentpacking where {pop sc_oldpacking setpacking}if end %%EndProlog %%BeginSetup md begin countdictstack[{ %%BeginFeature: *ManualFeed False statusdict /manualfeed false put %%EndFeature }featurecleanup countdictstack[{ %%BeginFeature: *InputSlot Cassette %%EndFeature }featurecleanup countdictstack[{ %%BeginFeature: *PageRegion LetterSmall lettersmall %%EndFeature }featurecleanup (peter)setjob /mT[1 0 0 -1 31 761]def /sD 16 dict def 300 level2{1 dict dup/WaitTimeout 4 -1 roll put setuserparams}{statusdict/waittimeout 3 -1 roll put}ifelse %%IncludeFont: Times-Bold %%IncludeFont: Times-Roman %%IncludeFont: Times-Italic %%IncludeFont: Times-BoldItalic %%IncludeFont: Symbol %%IncludeFont: TimesNewRomanPS-BoldMT %%IncludeFont: TimesNewRomanPS-BoldItalicMT /f0_1/Times-Bold :mre /f0_12 f0_1 12 scf /f0_10 f0_1 10 scf /f0_7 f0_1 7 scf /f1_1/Times-Roman :mre /f1_12 f1_1 12 scf /f1_11 f1_1 11 scf /f1_10 f1_1 10 scf /f1_7 f1_1 7 scf /f1_6 f1_1 6 scf /f2_1/Times-Italic :mre /f2_12 f2_1 12 scf /f2_10 f2_1 10 scf /f3_1 f1_1 :v def /f4_1/Times-BoldItalic :mre /f4_10 f4_1 10 scf /f5_1/Symbol :bsr 240/apple pd :esr /f5_12 f5_1 12 scf /f5_10 f5_1 10 scf /f5_6 f5_1 6 scf /f6_1 f5_1 def /f6_10 f6_1 10 scf /f7_1 f5_1 :mi /f7_10 f7_1 10 scf /f8_1 f1_1 1.087 scf /f8_10 f8_1 10 scf /f8_6 f8_1 6 scf /f9_1/TimesNewRomanPS-BoldMT :mre /f9_10 f9_1 10 scf /f9_6 f9_1 6 scf /f10_1/TimesNewRomanPS-BoldItalicMT :mre /f10_10 f10_1 10 scf /Courier findfont[10 0 0 -10 0 0]:mf setfont %%EndSetup %%Page: 1 1 %%BeginPageSetup initializepage (peter; page: 1 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 94 50 :M f0_12 sf 2.393 .239(Heuristic Greedy Search Algorithms for Latent Variable Models)J 92 75 :M f1_10 sf -.009(Peter Spirtes \(Department of Philosophy, Carnegie Mellon Univeristy, ps7z@andrew.cmu.edu\),)A 78 87 :M -.004(Thomas Richardson\(Department of Statistics, University of Washington\) , and Chris Meek \(Microsoft\))A 59 103 :M f0_10 sf (I)S 63 103 :M (.)S 67 103 :M 25.5 2.55( )J 95 103 :M .506(Introduction)A 59 119 :M f1_10 sf .255 .026(A )J 71 119 :M -.144(Bayesian )A 111 119 :M -.038(network )A 148 119 :M .465 .047(consists )J 186 119 :M .144 .014(of )J 200 119 :M .387 .039(two )J 221 119 :M .033 .003(distinct )J 256 119 :M .18 .018(parts: )J 284 119 :M .056 .006(a )J 294 119 :M -.337(directed )A 329 119 :M -.116(acyclic )A 362 119 :M -.053(graph )A 390 119 :M -.121(\(DAG )A 420 119 :M .144 .014(or )J 434 119 :M -.143(belief-network)A 59 131 :M -.064(structure\) and a set )A 137 131 :M .144 .014(of )J 149 131 :M -.136(parameters )A 195 131 :M -.052(for )A 210 131 :M .218 .022(the )J 226 131 :M .244 .024(DAG. )J 254 131 :M (The )S 273 131 :M -.053(DAG )A 298 131 :M .601 .06(in )J 310 131 :M .056 .006(a )J 318 131 :M -.144(Bayesian )A 357 131 :M -.038(network )A 393 131 :M -.126(can )A 410 131 :M .051 .005(be )J 423 131 :M -.207(used )A 444 131 :M .601 .06(to )J 456 131 :M -.205(represent)A 59 143 :M .515 .052(both )J 82 143 :M -.081(causal )A 111 143 :M .033 .003(hypotheses )J 160 143 :M -.313(and )A 178 143 :M .361 .036(sets )J 198 143 :M .144 .014(of )J 212 143 :M .295 .03(probability )J 262 143 :M .418 .042(distributions. )J 321 143 :M -.297(Under )A 350 143 :M .218 .022(the )J 368 143 :M -.081(causal )A 398 143 :M .055 .005(interpretation, )J 460 143 :M .056 .006(a )J 470 143 :M -.329(DAG)A 59 155 :M .068 .007(represents the causal relations in a given population with a set of vertices )J 356 155 :M f0_10 sf .951(V)A f1_10 sf .329 .033( )J 368 155 :M -.039(when )A 393 155 :M -.097(there )A 416 155 :M .694 .069(is )J 427 155 :M .051 .005(an )J 440 155 :M -.344(edge )A 461 155 :M .047 .005(from )J 484 155 :M (A)S 59 167 :M .058 .006(to B if and only if A is a direct cause of B relative to )J f0_10 sf (V)S f1_10 sf .075 .008(. \(We adopt the convention that sets of variables )J 480 167 :M -.602(are)A 59 179 :M -.164(capitalized )A 106 179 :M -.313(and )A 125 179 :M -.242(boldfaced, )A 170 179 :M -.313(and )A 189 179 :M -.105(individual )A 234 179 :M -.065(variables )A 275 179 :M -.235(are )A 292 179 :M -.164(capitalized )A 339 179 :M -.313(and )A 358 179 :M -.081(italicized.\) )A 405 179 :M -.297(Under )A 434 179 :M .218 .022(the )J 453 179 :M .024(statistical)A 59 191 :M -.026(interpretation )A 116 191 :M .056 .006(a )J 124 191 :M -.053(DAG )A 149 191 :M f2_10 sf .209(G)A f1_10 sf .072 .007( )J 160 191 :M -.126(can )A 177 191 :M .051 .005(be )J 190 191 :M -.031(taken )A 215 191 :M .601 .06(to )J 227 191 :M -.126(represent )A 266 191 :M .5 .05( )J 270 191 :M .056 .006(a )J 278 191 :M .303 .03(set )J 293 191 :M .144 .014(of )J 306 191 :M .388 .039(all )J 321 191 :M .218 .022(distributions )J 376 191 :M .388 .039(all )J 391 191 :M .144 .014(of )J 404 191 :M .043 .004(which )J 433 191 :M -.119(share )A 458 191 :M .056 .006(a )J 467 191 :M .303 .03(set )J 483 191 :M -.328(of)A 59 203 :M -.051(conditional independence relations that are entailed by satisfying a local directed Markov property )A 461 203 :M -.473(\(defined)A 59 215 :M -.044(below\).)A 59 231 :M .007 .001(Assumptions linking the statistical and causal interpretations of DAG are discussed in Spirtes, Glymour and)J 59 243 :M (Scheines )S 99 243 :M .203 .02(\(1993\). )J 133 243 :M .472 .047(For )J 152 243 :M .056 .006(a )J 161 243 :M -.081(particular )A 203 243 :M .303 .03(set )J 219 243 :M .144 .014(of )J 232 243 :M -.136(parameters )A 279 243 :M f5_10 sf .068(Q)A f1_10 sf ( )S 291 243 :M -.052(for )A 307 243 :M .056 .006(a )J 316 243 :M -.053(DAG )A 342 243 :M f2_10 sf .461(G)A f1_10 sf .29 .029(, )J 357 243 :M f2_10 sf .066(G)A f1_10 sf <28>S f5_10 sf .049(Q\))A f1_10 sf ( )S 383 243 :M .694 .069(is )J 395 243 :M .056 .006(a )J 404 243 :M -.124(parametric )A 451 243 :M .249 .025(family )J 483 243 :M -.328(of)A 59 255 :M .068(distributions.)A f5_10 sf ( )S 117 255 :M f1_10 sf .123 .012(Many )J 145 255 :M -.018(familiar )A 181 255 :M -.124(parametric )A 227 255 :M .068 .007(models, )J 263 255 :M .123 .012(such )J 286 255 :M .144 .014(as )J 299 255 :M -.113(non-recursive )A 357 255 :M -.026(structural )A 400 255 :M -.117(equation )A 439 255 :M -.064(models )A 473 255 :M .075(with)A 59 267 :M -.205(uncorrelated )A 110 267 :M -.044(errors, )A 139 267 :M -.135(factor )A 165 267 :M -.019(analytic )A 200 267 :M .068 .007(models, )J 235 267 :M .519 .052(item )J 258 267 :M -.06(response )A 297 267 :M .068 .007(models, )J 333 267 :M .246 .025(etc. )J 352 267 :M -.235(are )A 368 267 :M -.037(special )A 400 267 :M -.119(cases )A 425 267 :M .144 .014(of )J 438 267 :M -.302(parameterized)A 59 279 :M -.037(DAGs. Bayesian networks )A 168 279 :M -.094(have )A 190 279 :M -.211(proved )A 220 279 :M .042 .004(useful )J 248 279 :M .601 .06(in )J 260 279 :M -.081(expert )A 288 279 :M .743 .074(systems, )J 327 279 :M -.049(particularly )A 376 279 :M .517 .052(with )J 398 279 :M -.018(classification )A 454 279 :M -.03(problems)A 59 291 :M -.148(\(see )A 79 291 :M -.256(references )A 122 291 :M .601 .06(in )J 135 291 :M (Pearl )S 160 291 :M .115 .011(1988\) )J 188 291 :M -.313(and )A 206 291 :M .601 .06(in )J 219 291 :M -.104(predicting )A 263 291 :M .218 .022(the )J 280 291 :M -.163(effects )A 310 291 :M .144 .014(of )J 323 291 :M .127 .013(interventions )J 380 291 :M .674 .067(into )J 401 291 :M .189 .019(given )J 429 291 :M -.081(causal )A 459 291 :M .056(systems)A 59 303 :M .121 .012(\(Spirtes et al. 1993 and Pearl 1995\).)J 59 319 :M -.015(There has recently been significant progress in the development of algorithms for )A 387 319 :M -.033(learning )A 423 319 :M .218 .022(the )J 439 319 :M -.053(DAG )A 464 319 :M (part )S 483 319 :M -.328(of)A 59 331 :M .056 .006(a )J 67 331 :M -.144(Bayesian )A 106 331 :M -.038(network )A 142 331 :M .556 .056(without )J 177 331 :M .18 .018(latent )J 203 331 :M -.065(variables )A 242 331 :M .047 .005(from )J 265 331 :M -.289(data )A 284 331 :M -.313(and )A 301 331 :M .404 .04(optional )J 338 331 :M -.17(background )A 387 331 :M -.087(knowledge. )A 436 331 :M -.08(However, )A 479 331 :M -.108(the)A 59 343 :M -.016(problem of learning the DAG part of a Bayesian )A 255 343 :M -.038(network )A 291 343 :M .517 .052(with )J 313 343 :M .18 .018(latent )J 339 343 :M -.205(\(unmeasured\) )A 395 343 :M -.065(variables )A 434 343 :M .694 .069(is )J 445 343 :M .202 .02(much )J 471 343 :M -.182(more)A 59 355 :M .015 .001(difficult for two reasons: first the number of )J 239 355 :M .404 .04(possible )J 276 355 :M -.064(models )A 308 355 :M .694 .069(is )J 319 355 :M .59 .059(infinite, )J 355 355 :M -.313(and )A 372 355 :M -.109(second, )A 405 355 :M -.033(calculating )A 452 355 :M -.081(scores )A 480 355 :M -.328(for)A 59 367 :M -.008(latent variables models is generally much slower than calculating scores for models without latent variables.)A 59 383 :M .144 .014(In )J 71 383 :M .753 .075(this )J 90 383 :M -.141(paper )A 115 383 :M -.079(we )A 131 383 :M .676 .068(will )J 152 383 :M -.226(describe )A 188 383 :M .216 .022(how )J 210 383 :M .601 .06(to )J 223 383 :M -.193(extend )A 253 383 :M -.172(search )A 282 383 :M .366 .037(algorithms )J 330 383 :M -.288(developed )A 373 383 :M -.052(for )A 389 383 :M (non-latent )S 434 383 :M -.087(variable )A 470 383 :M -.329(DAG)A 59 395 :M -.014(models to the case of DAG models )A 202 395 :M .517 .052(with )J 224 395 :M .18 .018(latent )J 250 395 :M -.009(variables. )A 292 395 :M -.188(We )A 309 395 :M .676 .068(will )J 329 395 :M -.14(introduce )A 369 395 :M .387 .039(two )J 388 395 :M -.068(generalizations )A 451 395 :M .144 .014(of )J 463 395 :M (DAGs,)S 59 407 :M -.229(called )A 85 407 :M -.099(mixed )A 113 407 :M -.101(ancestor )A 149 407 :M -.026(graphs )A 179 407 :M -.052(\(or )A 194 407 :M (MAGs\) )S 228 407 :M -.313(and )A 245 407 :M (partial )S 274 407 :M -.101(ancestor )A 310 407 :M -.026(graphs )A 340 407 :M -.052(\(or )A 355 407 :M .491 .049(PAGs\), )J 389 407 :M -.313(and )A 407 407 :M -.021(briefly )A 438 407 :M -.226(describe )A 474 407 :M -.11(how)A 59 419 :M .202 .02(they )J 81 419 :M -.126(can )A 99 419 :M .051 .005(be )J 113 419 :M -.207(used )A 135 419 :M .601 .06(to )J 148 419 :M -.172(search )A 177 419 :M -.052(for )A 193 419 :M .18 .018(latent )J 220 419 :M -.087(variable )A 256 419 :M -.053(DAG )A 282 419 :M .068 .007(models, )J 318 419 :M .601 .06(to )J 331 419 :M .242 .024(classify, )J 369 419 :M -.313(and )A 388 419 :M .601 .06(to )J 402 419 :M -.18(predict )A 434 419 :M .218 .022(the )J 452 419 :M -.163(effects )A 483 419 :M -.328(of)A 59 431 :M .224 .022(interventions in causal systems.)J 59 447 :M f0_10 sf (I)S 63 447 :M (I)S 67 447 :M (.)S 71 447 :M 21.5 2.15( )J 95 447 :M 3.354 .335(Directed Acyclic Graphs \(DAGs\))J 59 463 :M f1_10 sf .681 .068(A )J f0_10 sf 1.891 .189(directed acyclic graph)J f1_10 sf 1.078 .108( \(DAG\) )J 209 463 :M f2_10 sf .209(G)A f1_10 sf .072 .007( )J 220 463 :M .517 .052(with )J 242 463 :M .056 .006(a )J 250 463 :M .303 .03(set )J 265 463 :M .144 .014(of )J 277 463 :M -.074(vertices )A 311 463 :M f0_10 sf .951(V)A f1_10 sf .329 .033( )J 323 463 :M -.126(can )A 340 463 :M .051 .005(be )J 353 463 :M .189 .019(given )J 379 463 :M .387 .039(two )J 398 463 :M .033 .003(distinct )J 431 463 :M -.017(interpretations.)A 59 475 :M -.235(\(We )A 79 475 :M -.119(place )A 103 475 :M .361 .036(sets )J 122 475 :M .144 .014(of )J 134 475 :M -.065(variables )A 173 475 :M -.313(and )A 190 475 :M -.355(defined )A 221 475 :M .192 .019(terms )J 247 475 :M .601 .06(in )J 259 475 :M -.175(boldface.\) )A 301 475 :M .234 .023(On )J 317 475 :M .218 .022(the )J 333 475 :M .047 .005(one )J 351 475 :M -.088(hand, )A 376 475 :M .123 .012(such )J 398 475 :M -.026(graphs )A 429 475 :M -.126(can )A 447 475 :M .051 .005(be )J 461 475 :M -.207(used )A 483 475 :M .222(to)A 59 487 :M -.026(represent causal relations between variables, where an edge from A to B in )A f2_10 sf (G)S f1_10 sf -.028( means that )A 415 487 :M .255 .026(A )J 426 487 :M .694 .069(is )J 437 487 :M .056 .006(a )J 445 487 :M -.21(direct )A 470 487 :M -.301(cause)A 59 499 :M .371 .037(of B relative to )J f0_10 sf .243(V)A f1_10 sf .207 .021(. A )J f0_10 sf .838 .084(causal graph)J f1_10 sf .489 .049( is a DAG given such an interpretation.)J 59 515 :M .06 .006(On the other hand, a DAG with a set of vertices )J f0_10 sf (V)S f1_10 sf .065 .006( can also represent a set of probability measures )J 459 515 :M -.067(over )A 480 515 :M f0_10 sf .951(V)A f1_10 sf (.)S 59 527 :M .196 .02(Following the terminology of Lauritzen )J f2_10 sf .135 .014(et al.)J f1_10 sf .114 .011( \(1990\) say that a )J 316 527 :M .295 .03(probability )J 364 527 :M -.116(measure )A 400 527 :M -.067(over )A 421 527 :M .056 .006(a )J 429 527 :M .303 .03(set )J 444 527 :M .144 .014(of )J 456 527 :M -.136(variables)A 59 539 :M f0_10 sf .455(V)A f1_10 sf .727 .073( satisfies the )J f0_10 sf 1.415 .141(local directed Markov property)J f1_10 sf .668 .067( for a directed )J 328 539 :M -.116(acyclic )A 359 539 :M -.053(graph )A 385 539 :M -.052(\(or )A 400 539 :M -.121(DAG\) )A 428 539 :M f2_10 sf .209(G)A f1_10 sf .072 .007( )J 439 539 :M .517 .052(with )J 461 539 :M -.156(vertices)A 59 551 :M f0_10 sf .951(V)A f1_10 sf .329 .033( )J 71 551 :M .328 .033(if )J 81 551 :M -.313(and )A 98 551 :M .515 .052(only )J 120 551 :M .328 .033(if )J 130 551 :M -.052(for )A 145 551 :M -.141(every )A 171 551 :M .056 .006(W )J 185 551 :M .601 .06(in )J 198 551 :M f0_10 sf 1.052(V)A f1_10 sf .662 .066(, )J 214 551 :M .056 .006(W )J 228 551 :M .694 .069(is )J 240 551 :M -.216(independent )A 291 551 :M .144 .014(of )J 304 551 :M f0_10 sf .59(V)A f1_10 sf .249<5C28>A f0_10 sf .396(Descendants)A f1_10 sf .272<28>A f2_10 sf .68(W)A f1_10 sf .433 .043(\) )J 397 551 :M f5_10 sf .62A f1_10 sf .202 .02( )J 410 551 :M f0_10 sf .299(Parents)A f1_10 sf .213<28>A f2_10 sf .533(W)A f1_10 sf .488 .049(\)\) )J 469 551 :M -.054(given)A 59 563 :M f0_10 sf .378(Parents)A f1_10 sf .269<28>A f2_10 sf .672(W)A f1_10 sf .56 .056(\), )J 117 563 :M -.185(where )A 144 563 :M f0_10 sf .35(Parents)A f1_10 sf .249<28>A f2_10 sf .623(W)A f1_10 sf .396 .04(\) )J 199 563 :M .694 .069(is )J 210 563 :M .218 .022(the )J 226 563 :M .303 .03(set )J 241 563 :M .144 .014(of )J 253 563 :M -.053(parents )A 286 563 :M .144 .014(of )J 299 563 :M f2_10 sf .902(W)A f1_10 sf .271 .027( )J 313 563 :M .601 .06(in )J 326 563 :M f2_10 sf .461(G)A f1_10 sf .29 .029(, )J 341 563 :M -.313(and )A 359 563 :M f0_10 sf .424(Descendants)A f1_10 sf .291<28>A f2_10 sf .729(W)A f1_10 sf .464 .046(\) )J 438 563 :M .694 .069(is )J 450 563 :M .218 .022(the )J 467 563 :M .303 .03(set )J 483 563 :M -.328(of)A 59 575 :M .117 .012(descendants of )J f2_10 sf .055(W)A f1_10 sf .035 .004( in )J f0_10 sf .052(G)A f1_10 sf .08 .008(. \(Note that a vertex is its own ancestor )J 311 575 :M -.313(and )A 328 575 :M -.22(descendant, )A 376 575 :M .28 .028(although )J 415 575 :M .555 .056(not )J 432 575 :M .811 .081(its )J 446 575 :M .216 .022(own )J 467 575 :M -.197(parent)A 59 587 :M -.015(or child.\) )A 99 587 :M .255 .026(A )J 110 587 :M -.053(DAG )A 135 587 :M f2_10 sf .209(G)A f1_10 sf .072 .007( )J 146 587 :M f0_10 sf .481(represents)A f1_10 sf .271 .027( )J 199 587 :M .218 .022(the )J 215 587 :M .303 .03(set )J 230 587 :M .144 .014(of )J 242 587 :M .295 .03(probability )J 290 587 :M -.087(measures )A 330 587 :M .043 .004(which )J 358 587 :M .235 .023(satisfy )J 388 587 :M .218 .022(the )J 404 587 :M .044 .004(local )J 427 587 :M -.337(directed )A 460 587 :M -.131(Markov)A 59 599 :M -.016(property for )A f2_10 sf (G)S f1_10 sf (.)S 59 615 :M (The )S 79 615 :M .133 .013(use )J 97 615 :M .144 .014(of )J 110 615 :M (DAGs )S 140 615 :M .601 .06(to )J 153 615 :M .397 .04(simultaneously )J 219 615 :M -.126(represent )A 259 615 :M .056 .006(a )J 268 615 :M .303 .03(set )J 284 615 :M .144 .014(of )J 297 615 :M -.081(causal )A 326 615 :M .033 .003(hypotheses )J 375 615 :M -.313(and )A 393 615 :M .056 .006(a )J 402 615 :M .249 .025(family )J 433 615 :M .144 .014(of )J 447 615 :M .012(probability)A 59 627 :M .218 .022(distributions )J 115 627 :M -.149(extends )A 150 627 :M -.094(back )A 174 627 :M .601 .06(to )J 189 627 :M .218 .022(the )J 208 627 :M .202 .02(path )J 232 627 :M -.144(diagrams )A 274 627 :M -.226(introduced )A 321 627 :M .417 .042(by )J 338 627 :M .18 .018(Sewell )J 372 627 :M .111 .011(Wright )J 407 627 :M .203 .02(\(1934\). )J 443 627 :M -.046(Variants )A 483 627 :M -.328(of)A 59 639 :M -.007(probabilistic DAG models were introduced in the 1980\325s in Pearl \(1988\) among others. )A 411 639 :M -.066(\(See )A 432 639 :M (Pearl )S 456 639 :M .357 .036(1988 )J 480 639 :M -.328(for)A 59 651 :M -.263(references.\))A endp %%Page: 2 2 %%BeginPageSetup initializepage (peter; page: 2 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 59 51 :M f0_10 sf (I)S 63 51 :M (I)S 67 51 :M (I)S 71 51 :M (.)S 75 51 :M 17.5 1.75( )J 95 51 :M 3.184 .318(Partial Ancestral Graphs \(PAGs\))J 59 67 :M f1_10 sf .026 .003(In some cases, not all of the variables in a DAG can be measured. We call those )J 383 67 :M -.065(variables )A 422 67 :M (whose )S 451 67 :M (values )S 480 67 :M -.602(are)A 59 79 :M -.023(measured the observed variables, and all other variables in the DAG latent variables. For a given )A 447 79 :M .153 .015(division )J 483 79 :M -.328(of)A 59 91 :M .218 .022(the )J 75 91 :M -.065(variables )A 114 91 :M .601 .06(in )J 126 91 :M .056 .006(a )J 135 91 :M -.053(DAG )A 161 91 :M .255 .026(G )J 173 91 :M .674 .067(into )J 194 91 :M -.199(observed )A 233 91 :M -.313(and )A 251 91 :M .464 .046(latent, )J 281 91 :M -.079(we )A 297 91 :M (write )S 322 91 :M f2_10 sf .147(G)A f1_10 sf .068<28>A f0_10 sf .158(O)A f1_10 sf .051(,)A f0_10 sf .136(L)A f1_10 sf .108 .011(\) )J 358 91 :M -.185(where )A 386 91 :M f0_10 sf .546(O)A f1_10 sf .175 .018( )J 399 91 :M .694 .069(is )J 411 91 :M .218 .022(the )J 428 91 :M .303 .03(set )J 444 91 :M .144 .014(of )J 457 91 :M -.299(observed)A 59 103 :M .063 .006(variables and )J f0_10 sf (L)S f1_10 sf .049 .005( is the set of latent variables.)J 59 119 :M 1.349 .135(A DAG )J f2_10 sf .748(G)A f1_10 sf .235 .024( )J f0_10 sf 1.922 .192(entails a)J f1_10 sf .235 .024( )J f0_10 sf 2.377 .238(conditional independence relation )J f1_10 sf .927 .093(if and only if it is )J 391 119 :M (true )S 410 119 :M .601 .06(in )J 422 119 :M -.141(every )A 447 119 :M .012(probability)A 59 131 :M .018 .002(measure satisfying the )J 152 131 :M .044 .004(local )J 175 131 :M -.337(directed )A 208 131 :M -.026(Markov )A 243 131 :M -.046(property )A 280 131 :M -.052(for )A 295 131 :M f2_10 sf .461(G)A f1_10 sf .29 .029(. )J 309 131 :M .132 .013(Two )J 331 131 :M -.337(directed )A 364 131 :M -.026(graphs )A 394 131 :M f2_10 sf .135(G)A f1_6 sf 0 2 rm .056(1)A 0 -2 rm f1_10 sf .062<28>A f0_10 sf .145(O)A f1_10 sf (,)S f0_10 sf .124(L)A f1_10 sf .099 .01(\) )J 432 131 :M -.313(and )A 449 131 :M f2_10 sf .271(G)A f1_6 sf 0 2 rm .113(2)A 0 -2 rm f1_10 sf .125<28>A f0_10 sf .209<4FD5>A f1_10 sf .094(,)A f0_10 sf .188<4CD5>A f1_10 sf <29>S 59 143 :M .781 .078(are )J f0_10 sf 2.104 .21(conditional independence equivalent)J f1_10 sf .642 .064( if and only if )J f0_10 sf .579(O)A f1_10 sf .344 .034( = )J f0_10 sf .413<4FD5>A f1_10 sf .682 .068(, and for all )J 388 143 :M f0_10 sf 1.052(X)A f1_10 sf .662 .066(, )J 403 143 :M f0_10 sf .951(Y)A f1_10 sf .329 .033( )J 415 143 :M -.313(and )A 432 143 :M f0_10 sf .604(Z)A f1_10 sf .226 .023( )J 443 143 :M -.242(included )A 479 143 :M .5 .05( )J 483 143 :M .222(in)A 59 155 :M f0_10 sf (O)S f1_10 sf (, )S f2_10 sf (G)S f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf .068 .007(\) entails )J f0_10 sf (X)S f1_10 sf .046 .005( and )J f0_10 sf (Y)S f1_10 sf .083 .008( are independent conditional on )J f0_10 sf (Z)S f1_10 sf .045 .004( if and )J 339 155 :M .515 .052(only )J 361 155 :M .328 .033(if )J 371 155 :M f2_10 sf .135(G)A f1_6 sf 0 2 rm .056(2)A 0 -2 rm f1_10 sf .062<28>A f0_10 sf .145(O)A f1_10 sf (,)S f0_10 sf .124(L)A f1_10 sf .099 .01(\) )J 409 155 :M .235 .023(entails )J 439 155 :M f0_10 sf .951(X)A f1_10 sf .329 .033( )J 451 155 :M -.313(and )A 468 155 :M f0_10 sf .951(Y)A f1_10 sf .329 .033( )J 480 155 :M -.602(are)A 59 167 :M -.216(independent )A 110 167 :M .5 .05( )J 116 167 :M -.045(conditional )A 166 167 :M .417 .042(on )J 182 167 :M f0_10 sf .76(Z)A f1_10 sf .518 .052(. )J 198 167 :M -.188(We )A 217 167 :M -.193(denote )A 248 167 :M .5 .05( )J 254 167 :M .218 .022(the )J 272 167 :M .303 .03(set )J 289 167 :M .144 .014(of )J 303 167 :M -.337(directed )A 338 167 :M .5 .05( )J 344 167 :M -.116(acyclic )A 377 167 :M -.026(graphs )A 409 167 :M .361 .036(that )J 430 167 :M -.235(are )A 447 167 :M -.099(conditional)A 59 179 :M .026 .003(independence equivalent to )J f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf (\) as )S f0_10 sf (Equiv)S f1_10 sf <28>S f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf (\)\).)S 59 195 :M .052 .005(A partial ancestral graph \(PAG\) can be used to represent subsets of )J f0_10 sf .018(Equiv)A f1_10 sf <28>S f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf .031 .003(\)\). A )J 410 195 :M .387 .039(PAG )J 434 195 :M .694 .069(is )J 445 195 :M .051 .005(an )J 458 195 :M -.442(extended)A 59 207 :M -.053(graph )A 86 207 :M .474 .047(consisting )J 132 207 :M .144 .014(of )J 145 207 :M .056 .006(a )J 154 207 :M .303 .03(set )J 170 207 :M .144 .014(of )J 183 207 :M -.074(vertices )A 218 207 :M f0_10 sf 1.052(V)A f1_10 sf .662 .066(, )J 234 207 :M -.313(and )A 252 207 :M .056 .006(a )J 261 207 :M .303 .03(set )J 277 207 :M .144 .014(of )J 290 207 :M -.253(edges )A 316 207 :M -.116(between )A 353 207 :M -.01(vertices, )A 391 207 :M -.185(where )A 419 207 :M -.097(there )A 443 207 :M .218 .022(may )J 465 207 :M .051 .005(be )J 479 207 :M -.108(the)A 59 219 :M .184 .018(following kinds of edges: A )J f5_10 sf .131A f1_10 sf .098 .01( B, A o)J f5_10 sf .126A f1_10 sf .112 .011(o B, A o)J f5_10 sf .124A f1_10 sf .086 .009( B, A )J 294 219 :M f5_10 sf .359A f1_10 sf .248 .025(o )J 313 219 :M .275 .028(B, )J 326 219 :M .255 .026(A )J 337 219 :M f5_10 sf .504A f1_10 sf .128 .013( )J 351 219 :M -.17(B )A 361 219 :M .144 .014(or )J 373 219 :M .5 .05( )J 377 219 :M .255 .026(A )J 388 219 :M f5_10 sf .504A f1_10 sf .128 .013( )J 402 219 :M .275 .028(B. )J 415 219 :M -.188(We )A 432 219 :M .133 .013(say )J 449 219 :M .361 .036(that )J 468 219 :M .218 .022(the )J 484 219 :M (A)S 59 231 :M .131 .013(endpoint of an A )J f5_10 sf .106A f1_10 sf .092 .009( B is \322\320\323; the )J 196 231 :M .255 .026(A )J 207 231 :M -.062(endpoint )A 245 231 :M .144 .014(of )J 257 231 :M .051 .005(an )J 270 231 :M .255 .026(A )J 281 231 :M f5_10 sf .065A f1_10 sf ( )S 295 231 :M .275 .028(B, )J 308 231 :M .255 .026(A )J 319 231 :M f5_10 sf .359A f1_10 sf .248 .025(o )J 338 231 :M .275 .028(B, )J 351 231 :M .144 .014(or )J 363 231 :M .255 .026(A )J 374 231 :M f5_10 sf .504A f1_10 sf .128 .013( )J 388 231 :M -.17(B )A 398 231 :M -.344(edge )A 419 231 :M .694 .069(is )J 430 231 :M .146 .015J 451 231 :M -.313(and )A 468 231 :M .218 .022(the )J 484 231 :M (A)S 59 243 :M .12 .012(endpoint of a A o)J f5_10 sf .098A f1_10 sf .082 .008(o B or A o)J f5_10 sf .096A f1_10 sf .123 .012( B is \322o\323. The conventions )J 303 243 :M -.052(for )A 318 243 :M .218 .022(the )J 334 243 :M -.17(B )A 344 243 :M -.043(endpoints )A 386 243 :M -.235(are )A 401 243 :M .228 .023(analogous. )J 448 243 :M .144 .014(In )J 460 243 :M -.253(addition)A 59 255 :M .044 .004(pairs )J 82 255 :M .144 .014(of )J 94 255 :M -.344(edge )A 115 255 :M -.043(endpoints )A 157 255 :M .218 .022(may )J 178 255 :M .051 .005(be )J 191 255 :M -.226(connected )A 233 255 :M .417 .042(by )J 247 255 :M -.008(underlining. )A 300 255 :M .255 .026(A )J 312 255 :M (partial )S 342 255 :M -.114(ancestral )A 381 255 :M -.053(graph )A 408 255 :M -.052(for )A 424 255 :M .056 .006(a )J 433 255 :M .303 .03(set )J 449 255 :M .144 .014(of )J 462 255 :M -.457(directed)A 59 267 :M -.032(acyclic graphs )A f0_10 sf -.062(G)A f1_10 sf -.033( each sharing the same set of observed )A 282 267 :M -.065(variables )A 321 267 :M f0_10 sf .744(O)A f1_10 sf .435 .043(, )J 336 267 :M .098 .01(contains )J 373 267 :M (partial )S 402 267 :M .139 .014(information )J 453 267 :M .189 .019(about )J 479 267 :M -.108(the)A 59 279 :M .163 .016(ancestor relations in )J f0_10 sf .079(G)A f1_10 sf .154 .015(, namely only those ancestor relations common to all members of )J f0_10 sf .079(G)A f1_10 sf .106 .011(. \(If we allow )J 483 279 :M f0_10 sf (G)S 59 291 :M f1_10 sf -.074(to contain directed cyclic graphs as well as directed acyclic graphs then several )A 373 291 :M (more )S 397 291 :M -.213(different )A 433 291 :M -.033(kinds )A 458 291 :M .144 .014(of )J 470 291 :M -.442(edges)A 59 303 :M -.052(are needed in the PAG. See Richardson, )A 221 303 :M .115 .011(1996\) )J 248 303 :M .144 .014(In )J 260 303 :M .218 .022(the )J 276 303 :M .325 .033(following )J 319 303 :M .057 .006(definition, )J 364 303 :M .043 .004(which )J 392 303 :M -.117(provides )A 429 303 :M .056 .006(a )J 437 303 :M .037 .004(semantics )J 480 303 :M -.328(for)A 59 315 :M .438 .044(PAGs )J 88 315 :M -.079(we )A 104 315 :M .133 .013(use )J 122 315 :M -.126A 140 315 :M .144 .014(as )J 153 315 :M .056 .006(a )J 162 315 :M .139 .014(meta-symbol )J 219 315 :M -.049(indicating )A 263 315 :M .218 .022(the )J 280 315 :M -.184(presence )A 318 315 :M .144 .014(of )J 331 315 :M .047 .005(any )J 350 315 :M .047 .005(one )J 369 315 :M .144 .014(of )J 382 315 :M 2 .2({o,\312\320, )J 412 315 :M .431 .043(>}, )J 430 315 :M .758 .076(e.g. )J 450 315 :M .951(A)A f0_10 sf .329 .033( )J 464 315 :M f5_10 sf .27<2AAE>A f1_10 sf .091 .009( )J 485 315 :M (B)S 59 327 :M .146 .015(represents either A )J f5_10 sf .109A f1_10 sf .073 .007( B, A )J f5_10 sf .115A f1_10 sf .088 .009( B, or A o)J f5_10 sf .109A f1_10 sf .108 .011( B.)J 59 343 :M f0_10 sf 2.78 .278(Partial Ancestral Graphs)J f1_10 sf .551 .055( \()J f0_10 sf .709(PAGs)A f1_10 sf <29>S 59 359 :M .1 .01(If )J f0_10 sf .111(G)A f1_10 sf .166 .017( is a set of directed acyclic graphs included in )J f0_10 sf .073(Equiv)A f1_10 sf <28>S f2_10 sf .103(G)A f1_10 sf <28>S f0_10 sf .111(O)A f1_10 sf (,)S f0_10 sf .109 .011( L)J f1_10 sf .118 .012(\)\), )J f6_10 sf .113(Y)A f1_10 sf .123 .012( is a PAG for )J f0_10 sf .111(G)A f1_10 sf .143 .014( if and only if)J 77 375 :M -.003(\(i\) There is an edge between A and B in )A f6_10 sf (Y)S f1_10 sf -.003( if and only if every DAG in )A f0_10 sf (G)S f1_10 sf ( does )S 395 375 :M .555 .056(not )J 412 375 :M .18 .018(entail )J 438 375 :M .361 .036(that )J 457 375 :M .255 .026(A )J 468 375 :M -.313(and )A 485 375 :M (B)S 77 387 :M -.062(are independent conditional on any subset of )A f0_10 sf -.119(O)A f1_10 sf -.08(\\{A,B}.)A 77 403 :M .224 .022(\(ii\) If there is an edge in )J f6_10 sf .193 .019(Y )J f1_10 sf .238 .024(out of A, i.e. A)J f0_10 sf .05 .005( )J f5_10 sf .218A f1_10 sf .236 .024( B, then A is an ancestor of B in every graph in )J f0_10 sf .172(G)A f1_10 sf (.)S 77 419 :M .259 .026(\(iii\) If there is an edge in )J f6_10 sf .219 .022(Y )J f1_10 sf .296 .03(into B, i.e. A)J f5_10 sf .187<2AAE>A f1_10 sf .274 .027( B, then in every DAG in )J f0_10 sf .196(G)A f1_10 sf .159 .016(, B is )J f0_10 sf .117(not)A f1_10 sf .313 .031( an ancestor of A.)J 77 435 :M -.015(\(iv\) If there is an underlining A*\321)A 217 0 5 730 rC 217 435 :M 10 f3_1 :p 3 :m .5 .05( )J 219 435 :M 6 :m .476 .048( )J gR gS 0 0 552 730 rC 217 435 :M f1_10 sf 10 f3_1 :p 16 :m -.335(*B*)A 228 0 5 730 rC 228 435 :M 3 :m .5 .05( )J 230 435 :M 6 :m .476 .048( )J gR gS 0 0 552 730 rC 233 435 :M f1_10 sf .322 .032(\321*C in )J f6_10 sf .201(Y)A f1_10 sf .272 .027( then B is an ancestor )J 368 435 :M .144 .014(of )J 380 435 :M (\(at )S 394 435 :M .118 .012(least )J 416 435 :M .047 .005(one )J 434 435 :M -.052(of\) )A 449 435 :M .255 .026(A )J 460 435 :M .144 .014(or )J 472 435 :M .755 .075(C )J 483 435 :M .222(in)A 77 448 :M .115 .012(every DAG in )J f0_10 sf .065(G)A f1_10 sf (.)S 77 464 :M .063 .006(\(v\) Any edge endpoint not marked in one of the above ways is left with a small circle thus: o\321*.)J 59 480 :M .517 .052(Some )J 86 480 :M -.033(examples )A 127 480 :M .144 .014(of )J 139 480 :M .438 .044(PAGs )J 167 480 :M -.235(are )A 182 480 :M .261 .026(shown )J 212 480 :M .601 .06(in )J 224 480 :M .248 .025(Figure )J 254 480 :M .833 .083(1, )J 266 480 :M -.185(where )A 293 480 :M f0_10 sf .546(O)A f1_10 sf .175 .018( )J 305 480 :M -.14(= )A 314 480 :M .061 .006({A,B,C,D}. )J 366 480 :M .144 .014(In )J 379 480 :M -.119(cases )A 404 480 :M -.185(where )A 432 480 :M .218 .022(the )J 449 480 :M -.022(distinction)A 59 492 :M -.116(between )A 95 492 :M .18 .018(latent )J 121 492 :M -.065(variables )A 160 492 :M -.313(and )A 177 492 :M -.226(measured )A 217 492 :M -.065(variables )A 256 492 :M .694 .069(is )J 267 492 :M .56 .056(important, )J 314 492 :M -.079(we )A 330 492 :M -.069(enclose )A 364 492 :M .18 .018(latent )J 391 492 :M -.065(variables )A 431 492 :M .601 .06(in )J 444 492 :M .559 .056(ovals. )J 473 492 :M -.291(\(The)A 59 504 :M -.003(MAGs in Figure 1 are defined in the next section.\))A 59 520 :M (The )S 78 520 :M -.164(requirement )A 128 520 :M .361 .036(that )J 147 520 :M f0_10 sf .546(G)A f1_10 sf .175 .018( )J 159 520 :M .694 .069(is )J 170 520 :M -.242(included )A 206 520 :M .601 .06(in )J 218 520 :M f0_10 sf .37(Equiv)A f1_10 sf .241<28>A f2_10 sf .523(G)A f1_10 sf .241<28>A f0_10 sf .563(O)A f1_10 sf .181(,)A f0_10 sf .181 .018( )J 276 520 :M .074(L)A f1_10 sf .084 .008(\)\) )J 294 520 :M -.125(guarantees )A 340 520 :M .361 .036(that )J 360 520 :M .328 .033(if )J 371 520 :M .047 .005(one )J 390 520 :M -.337(directed )A 424 520 :M -.116(acyclic )A 456 520 :M -.053(graph )A 483 520 :M .222(in)A 59 532 :M f0_10 sf .107(Equiv)A f1_10 sf .07<28>A f2_10 sf .151(G)A f1_10 sf .07<28>A f0_10 sf .163(O)A f1_10 sf .052(,)A f0_10 sf .16 .016( L)J f1_10 sf .232 .023(\)\) does not entail that A and B )J 246 532 :M -.235(are )A 261 532 :M -.216(independent )A 311 532 :M -.045(conditional )A 359 532 :M .417 .042(on )J 373 532 :M .047 .005(any )J 391 532 :M .315 .032(subset )J 420 532 :M .144 .014(of )J 432 532 :M f0_10 sf -.102(O)A f1_10 sf -.063(\\{A,B}, )A 474 532 :M -.072(then)A 59 544 :M -.017(all directed acyclic graphs in )A f0_10 sf -.024(Equiv)A f1_10 sf <28>S f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf ( L)S f1_10 sf -.018(\)\) do not entail that A and B are independent conditional )A 463 544 :M .417 .042(on )J 477 544 :M -.219(any)A 59 556 :M -.018(subset of )A f0_10 sf (O)S f1_10 sf -.025(\\{A,B}.)A endp %%Page: 3 3 %%BeginPageSetup initializepage (peter; page: 3 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 104 44 342 133 rC gS .77 .775 scale 135.142 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 137.741 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 140.34 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 144.238 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 146.837 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 149.436 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 153.334 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 155.933 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 158.532 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 161.131 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 165.029 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 167.628 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 170.227 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 174.125 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 176.724 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 179.323 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 183.221 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 185.82 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 188.419 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 192.317 65.784 :M f1_12 sf ( )S gR gS .77 .775 scale 194.916 65.784 :M f1_12 sf (T)S gR gS .77 .775 scale 135.142 90.291 :M f1_12 sf (A)S gR gS .77 .775 scale 142.938 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 145.537 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 148.136 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 152.035 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 154.633 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 157.232 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 161.131 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 163.73 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 166.328 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 170.227 90.291 :M f5_12 sf ( )S gR gS .77 .775 scale 172.826 90.291 :M f1_12 sf (B)S gR gS .77 .775 scale 180.622 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 183.221 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 187.119 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 189.718 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 192.317 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 196.216 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 198.814 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 201.413 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 205.312 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 207.911 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 210.509 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 213.108 90.291 :M f1_12 sf (C)S gR gS .77 .775 scale 222.204 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 224.803 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 227.402 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 231.3 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 233.899 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 236.498 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 239.097 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 242.995 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 245.594 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 248.193 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 252.092 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 254.69 90.291 :M f1_12 sf (D)S gR gS .77 .775 scale 262.487 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 265.086 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 268.984 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 271.583 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 274.182 90.291 :M f1_12 sf (A)S gR gS .77 .775 scale 283.278 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 285.877 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 288.476 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 291.075 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 294.973 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 297.572 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 300.171 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 304.069 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 306.668 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 309.267 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 313.165 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 315.764 90.291 :M f1_12 sf (B)S gR gS .77 .775 scale 323.561 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 326.16 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 330.058 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 332.657 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 335.256 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 339.154 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 341.753 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 344.352 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 348.25 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 350.849 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 353.448 90.291 :M f1_12 sf (C)S gR gS .77 .775 scale 361.245 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 365.143 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 367.742 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 370.341 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 374.239 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 376.838 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 379.437 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 383.335 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 385.934 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 388.533 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 391.132 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 395.03 90.291 :M f1_12 sf (D)S gR gS .77 .775 scale 402.827 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 405.426 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 409.324 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 411.923 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 414.522 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 417.121 90.291 :M f1_12 sf (A)S gR gS .77 .775 scale 426.217 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 428.815 90.291 :M f1_12 sf (o)S gR gS .77 .775 scale 435.313 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 437.912 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 440.51 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 443.109 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 447.008 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 449.607 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 452.205 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 456.104 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 458.703 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 461.301 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 465.2 90.291 :M f1_12 sf (B)S gR gS .77 .775 scale 472.996 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 475.595 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 478.194 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 482.093 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 484.691 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 487.29 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 491.189 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 493.788 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 496.386 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 500.285 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 502.884 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 505.482 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 508.081 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 511.98 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 514.579 90.291 :M f1_12 sf (C)S gR gS .77 .775 scale 522.375 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 526.274 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 528.872 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 531.471 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 534.07 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 537.969 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 540.567 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 543.166 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 547.065 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 549.663 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 552.262 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 556.161 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 558.76 90.291 :M f1_12 sf (o)S gR gS .77 .775 scale 565.257 90.291 :M f1_12 sf ( )S gR gS .77 .775 scale 567.856 90.291 :M f1_12 sf (D)S gR gS .77 .775 scale 135.142 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 137.741 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 140.34 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 144.238 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 146.837 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 149.436 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 153.334 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 155.933 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 158.532 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 161.131 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 165.029 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 167.628 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 170.227 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 174.125 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 176.724 113.509 :M f1_12 sf (D)S gR gS .77 .775 scale 184.521 113.509 :M f1_12 sf (A)S gR gS .77 .775 scale 192.317 113.509 :M f1_12 sf (G)S gR gS .77 .775 scale 201.413 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 205.312 113.509 :M f2_12 sf (G)S gR gS .77 .775 scale 213.108 117.379 :M f1_7 sf (1)S gR gS .77 .775 scale 218.306 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 220.905 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 223.504 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 226.103 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 230.001 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 232.6 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 235.199 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 239.097 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 241.696 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 244.295 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 248.193 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 250.792 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 253.391 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 257.289 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 259.888 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 262.487 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 265.086 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 268.984 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 271.583 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 274.182 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 278.08 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 280.679 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 283.278 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 287.176 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 289.775 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 292.374 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 296.273 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 298.871 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 301.47 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 304.069 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 307.967 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 310.566 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 313.165 113.509 :M f1_12 sf (M)S gR gS .77 .775 scale 323.561 113.509 :M f1_12 sf (A)S gR gS .77 .775 scale 331.357 113.509 :M f1_12 sf (G)S gR gS .77 .775 scale 340.454 113.509 :M f1_12 sf <28>S gR gS .77 .775 scale 344.352 113.509 :M f2_12 sf (G)S gR gS .77 .775 scale 353.448 117.379 :M f1_7 sf (1)S gR gS .77 .775 scale 357.346 113.509 :M f1_12 sf <28>S gR gS .77 .775 scale 361.245 113.509 :M f0_12 sf (O)S gR gS .77 .775 scale 370.341 113.509 :M f1_12 sf (,)S gR gS .77 .775 scale 374.239 113.509 :M f0_12 sf (L)S gR gS .77 .775 scale 383.335 113.509 :M f1_12 sf <29>S gR gS .77 .775 scale 387.233 113.509 :M f1_12 sf <29>S gR gS .77 .775 scale 391.132 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 393.731 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 396.329 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 400.228 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 402.827 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 405.426 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 409.324 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 411.923 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 414.522 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 417.121 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 421.019 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 423.618 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 426.217 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 430.115 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 432.714 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 435.313 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 439.211 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 441.81 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 444.409 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 448.307 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 450.906 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 453.505 113.509 :M f1_12 sf ( )S gR gS .77 .775 scale 456.104 113.509 :M f1_12 sf (P)S gR gS .77 .775 scale 463.9 113.509 :M f1_12 sf (A)S gR gS .77 .775 scale 471.697 113.509 :M f1_12 sf (G)S gR gS .77 .775 scale 480.793 113.509 :M f1_12 sf <28>S gR gS .77 .775 scale 484.691 113.509 :M f0_12 sf (E)S gR gS .77 .775 scale 492.488 113.509 :M f0_12 sf (q)S gR gS .77 .775 scale 500.285 113.509 :M f0_12 sf (u)S gR gS .77 .775 scale 506.782 113.509 :M f0_12 sf (i)S gR gS .77 .775 scale 510.68 113.509 :M f0_12 sf (v)S gR gS .77 .775 scale 517.177 113.509 :M f1_12 sf <28>S gR gS .77 .775 scale 521.076 113.509 :M f2_12 sf (G)S gR gS .77 .775 scale 530.172 117.379 :M f1_7 sf (1)S gR gS .77 .775 scale 534.07 113.509 :M f1_12 sf <28>S gR gS .77 .775 scale 539.268 113.509 :M f0_12 sf (O)S gR gS .77 .775 scale 547.065 113.509 :M f1_12 sf (,)S gR gS .77 .775 scale 552.262 113.509 :M f0_12 sf (L)S gR gS .77 .775 scale 560.059 113.509 :M f1_12 sf <29>S gR gS .77 .775 scale 563.957 113.509 :M f1_12 sf <29>S gR gS .77 .775 scale 135.142 138.017 :M f1_12 sf (A)S gR gS .77 .775 scale 278.08 138.017 :M f1_12 sf (A)S gR gS .77 .775 scale 314.465 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 317.064 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 320.962 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 323.561 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 326.16 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 330.058 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 332.657 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 335.256 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 339.154 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 341.753 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 344.352 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 348.25 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 350.849 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 353.448 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 356.047 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 359.945 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 362.544 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 365.143 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 369.041 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 371.64 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 374.239 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 378.137 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 380.736 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 383.335 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 387.233 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 389.832 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 392.431 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 396.329 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 398.928 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 401.527 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 404.126 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 408.024 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 410.623 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 413.222 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 417.121 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 419.719 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 422.318 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 426.217 138.017 :M f1_12 sf ( )S gR gS .77 .775 scale 428.815 138.017 :M f1_12 sf (A)S gR gS .77 .775 scale 436.612 138.017 :M f1_12 sf (o)S gR gS .77 .775 scale 135.142 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 137.741 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 140.34 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 144.238 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 146.837 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 149.436 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 153.334 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 155.933 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 158.532 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 161.131 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 165.029 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 167.628 161.234 :M f1_12 sf (B)S gR gS .77 .775 scale 175.425 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 179.323 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 181.922 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 184.521 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 187.119 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 191.018 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 193.617 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 196.216 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 200.114 161.234 :M f1_12 sf (D)S gR gS .77 .775 scale 314.465 161.234 :M f1_12 sf (B)S gR gS .77 .775 scale 350.849 161.234 :M f1_12 sf (D)S gR gS .77 .775 scale 358.646 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 361.245 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 365.143 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 367.742 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 370.341 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 374.239 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 376.838 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 379.437 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 383.335 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 385.934 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 388.533 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 391.132 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 395.03 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 397.629 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 400.228 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 404.126 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 406.725 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 409.324 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 413.222 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 415.821 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 418.42 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 422.318 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 424.917 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 427.516 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 430.115 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 434.013 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 436.612 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 439.211 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 443.109 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 445.708 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 448.307 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 452.205 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 454.804 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 457.403 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 461.301 161.234 :M f1_12 sf (B)S gR gS .77 .775 scale 469.098 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 471.697 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 474.296 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 478.194 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 480.793 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 483.392 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 487.29 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 489.889 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 492.488 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 495.087 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 498.985 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 501.584 161.234 :M f1_12 sf ( )S gR gS .77 .775 scale 504.183 161.234 :M f1_12 sf (D)S gR gS .77 .775 scale 135.142 185.742 :M f1_12 sf (C)S gR gS .77 .775 scale 278.08 185.742 :M f1_12 sf (C)S gR gS .77 .775 scale 350.849 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 353.448 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 356.047 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 359.945 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 362.544 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 365.143 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 369.041 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 371.64 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 374.239 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 378.137 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 380.736 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 383.335 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 387.233 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 389.832 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 392.431 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 396.329 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 398.928 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 401.527 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 404.126 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 408.024 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 410.623 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 413.222 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 417.121 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 419.719 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 422.318 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 426.217 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 428.815 185.742 :M f1_12 sf ( )S gR gS .77 .775 scale 431.414 185.742 :M f1_12 sf (C)S gR gS .77 .775 scale 439.211 185.742 :M f1_12 sf (o)S gR gS .77 .775 scale 135.142 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 137.741 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 140.34 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 144.238 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 146.837 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 149.436 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 153.334 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 155.933 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 158.532 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 161.131 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 165.029 210.25 :M f1_12 sf (D)S gR gS .77 .775 scale 172.826 210.25 :M f1_12 sf (A)S gR gS .77 .775 scale 180.622 210.25 :M f1_12 sf (G)S gR gS .77 .775 scale 189.718 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 192.317 210.25 :M f2_12 sf (G)S gR gS .77 .775 scale 201.413 212.829 :M f1_7 sf (2)S gR gS .77 .775 scale 205.312 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 209.21 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 211.809 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 214.408 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 218.306 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 220.905 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 223.504 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 226.103 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 230.001 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 232.6 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 235.199 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 239.097 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 241.696 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 244.295 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 248.193 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 250.792 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 253.391 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 257.289 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 259.888 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 262.487 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 265.086 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 268.984 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 271.583 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 274.182 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 278.08 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 280.679 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 283.278 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 287.176 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 289.775 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 292.374 210.25 :M f1_12 sf (M)S gR gS .77 .775 scale 302.77 210.25 :M f1_12 sf (A)S gR gS .77 .775 scale 310.566 210.25 :M f1_12 sf (G)S gR gS .77 .775 scale 319.662 210.25 :M f1_12 sf <28>S gR gS .77 .775 scale 323.561 210.25 :M f2_12 sf (G)S gR gS .77 .775 scale 332.657 212.829 :M f1_7 sf (2)S gR gS .77 .775 scale 336.555 210.25 :M f1_12 sf <28>S gR gS .77 .775 scale 340.454 210.25 :M f0_12 sf (O)S gR gS .77 .775 scale 349.55 210.25 :M f1_12 sf (,)S gR gS .77 .775 scale 353.448 210.25 :M f0_12 sf (L)S gR gS .77 .775 scale 361.245 210.25 :M f1_12 sf <29>S gR gS .77 .775 scale 365.143 210.25 :M f1_12 sf <29>S gR gS .77 .775 scale 370.341 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 372.94 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 375.538 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 378.137 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 382.036 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 384.634 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 387.233 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 391.132 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 393.731 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 396.329 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 400.228 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 402.827 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 405.426 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 409.324 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 411.923 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 414.522 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 417.121 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 421.019 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 423.618 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 426.217 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 430.115 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 432.714 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 435.313 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 439.211 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 441.81 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 444.409 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 448.307 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 450.906 210.25 :M f1_12 sf ( )S gR gS .77 .775 scale 453.505 210.25 :M f1_12 sf (P)S gR gS .77 .775 scale 461.301 210.25 :M f1_12 sf (A)S gR gS .77 .775 scale 469.098 210.25 :M f1_12 sf (G)S gR gS .77 .775 scale 478.194 210.25 :M f1_12 sf <28>S gR gS .77 .775 scale 482.093 210.25 :M f0_12 sf (E)S gR gS .77 .775 scale 489.889 210.25 :M f0_12 sf (q)S gR gS .77 .775 scale 496.386 210.25 :M f0_12 sf (u)S gR gS .77 .775 scale 504.183 210.25 :M f0_12 sf (i)S gR gS .77 .775 scale 508.081 210.25 :M f0_12 sf (v)S gR gS .77 .775 scale 514.579 210.25 :M f1_12 sf <28>S gR gS .77 .775 scale 518.477 210.25 :M f2_12 sf (G)S gR gS .77 .775 scale 527.573 212.829 :M f1_7 sf (2)S gR gS .77 .775 scale 531.471 210.25 :M f1_12 sf <28>S gR gS .77 .775 scale 535.37 210.25 :M f0_12 sf (O)S gR gS .77 .775 scale 544.466 210.25 :M f1_12 sf (,)S gR gS .77 .775 scale 548.364 210.25 :M f0_12 sf (L)S gR gS .77 .775 scale 556.161 210.25 :M f1_12 sf <29>S gR gS .77 .775 scale 560.059 210.25 :M f1_12 sf <29>S gR gR gS 103 41 344 136 rC -1 -1 143 61 1 1 151 51 @b np 145 60 :M 141 57 :L 139 63 :L 145 60 :L eofill 141 58 -1 1 146 60 1 141 57 @a -1 -1 140 64 1 1 141 57 @b -1 -1 140 64 1 1 145 60 @b 155 53 -1 1 162 58 1 155 52 @a np 162 55 :M 158 59 :L 165 61 :L 162 55 :L eofill -1 -1 159 60 1 1 162 55 @b 158 60 -1 1 166 61 1 158 59 @a 162 56 -1 1 166 61 1 162 55 @a 181 68 -1 1 195 67 1 181 67 @a np 182 70 :M 182 63 :L 176 67 :L 182 70 :L eofill -1 -1 183 71 1 1 182 63 @b -1 -1 177 68 1 1 182 63 @b 176 68 -1 1 183 70 1 176 67 @a 223 68 -1 1 235 67 1 223 67 @a np 232 63 :M 232 70 :L 238 67 :L 232 63 :L eofill -1 -1 233 71 1 1 232 63 @b -1 -1 233 71 1 1 238 67 @b 232 64 -1 1 239 67 1 232 63 @a 258 68 -1 1 267 67 1 258 67 @a np 265 63 :M 265 70 :L 271 67 :L 265 63 :L eofill -1 -1 266 71 1 1 265 63 @b -1 -1 266 71 1 1 271 67 @b 265 64 -1 1 272 67 1 265 63 @a np 260 70 :M 260 63 :L 254 67 :L 260 70 :L eofill -1 -1 261 71 1 1 260 63 @b -1 -1 255 68 1 1 260 63 @b 254 68 -1 1 261 70 1 254 67 @a 288 68 -1 1 303 67 1 288 67 @a np 290 70 :M 290 63 :L 284 67 :L 290 70 :L eofill -1 -1 291 71 1 1 290 63 @b -1 -1 285 68 1 1 290 63 @b 284 68 -1 1 291 70 1 284 67 @a 113 107 -1 1 125 115 1 113 106 @a np 125 112 :M 121 117 :L 128 119 :L 125 112 :L eofill -1 -1 122 118 1 1 125 112 @b 121 118 -1 1 129 119 1 121 117 @a 125 113 -1 1 129 119 1 125 112 @a -1 -1 115 140 1 1 126 130 @b np 123 129 :M 127 133 :L 130 127 :L 123 129 :L eofill 123 130 -1 1 128 133 1 123 129 @a -1 -1 128 134 1 1 130 127 @b -1 -1 124 130 1 1 130 127 @b 138 123 -1 1 148 122 1 138 122 @a np 145 119 :M 145 126 :L 151 122 :L 145 119 :L eofill -1 -1 146 127 1 1 145 119 @b -1 -1 146 127 1 1 151 122 @b 145 120 -1 1 152 122 1 145 119 @a 253 123 -1 1 263 122 1 253 122 @a np 261 119 :M 261 125 :L 267 122 :L 261 119 :L eofill -1 -1 262 126 1 1 261 119 @b -1 -1 262 126 1 1 267 122 @b 261 120 -1 1 268 122 1 261 119 @a 227 108 -1 1 239 116 1 227 107 @a np 238 113 :M 235 118 :L 242 119 :L 238 113 :L eofill -1 -1 236 119 1 1 238 113 @b 235 119 -1 1 243 119 1 235 118 @a 238 114 -1 1 243 119 1 238 113 @a -1 -1 226 138 1 1 238 128 @b np 235 126 :M 238 131 :L 242 125 :L 235 126 :L eofill 235 127 -1 1 239 131 1 235 126 @a -1 -1 239 132 1 1 242 125 @b -1 -1 236 127 1 1 242 125 @b 118 68 -1 1 128 67 1 118 67 @a np 125 63 :M 125 70 :L 131 67 :L 125 63 :L eofill -1 -1 126 71 1 1 125 63 @b -1 -1 126 71 1 1 131 67 @b 125 64 -1 1 132 67 1 125 63 @a 29 10 156 46.5 @f 334 68 -1 1 346 67 1 334 67 @a np 343 63 :M 343 70 :L 349 67 :L 343 63 :L eofill -1 -1 344 71 1 1 343 63 @b -1 -1 344 71 1 1 349 67 @b 343 64 -1 1 350 67 1 343 63 @a 375 68 -1 1 383 67 1 375 67 @a np 381 63 :M 381 70 :L 387 67 :L 381 63 :L eofill -1 -1 382 71 1 1 381 63 @b -1 -1 382 71 1 1 387 67 @b 381 64 -1 1 388 67 1 381 63 @a np 376 70 :M 376 63 :L 370 67 :L 376 70 :L eofill -1 -1 377 71 1 1 376 63 @b -1 -1 371 68 1 1 376 63 @b 370 68 -1 1 377 70 1 370 67 @a 417 68 -1 1 431 67 1 417 67 @a np 419 70 :M 419 63 :L 412 67 :L 419 70 :L eofill -1 -1 420 71 1 1 419 63 @b -1 -1 413 68 1 1 419 63 @b 412 68 -1 1 420 70 1 412 67 @a 339 107 -1 1 351 115 1 339 106 @a np 351 112 :M 348 117 :L 354 119 :L 351 112 :L eofill -1 -1 349 118 1 1 351 112 @b 348 118 -1 1 355 119 1 348 117 @a 351 113 -1 1 355 119 1 351 112 @a -1 -1 343 140 1 1 355 130 @b np 352 129 :M 355 133 :L 358 127 :L 352 129 :L eofill 352 130 -1 1 356 133 1 352 129 @a -1 -1 356 134 1 1 358 127 @b -1 -1 353 130 1 1 358 127 @b 367 123 -1 1 377 122 1 367 122 @a np 375 119 :M 375 126 :L 381 122 :L 375 119 :L eofill -1 -1 376 127 1 1 375 119 @b -1 -1 376 127 1 1 381 122 @b 375 120 -1 1 382 122 1 375 119 @a gR gS 0 0 552 730 rC 254 187 :M f0_10 sf 3.634 .363(Figure 1)J 59 203 :M f1_10 sf -.025(Note that only condition \(i\) gives necessary and sufficient conditions about features )A 395 203 :M .144 .014(of )J 407 203 :M .218 .022(the )J 423 203 :M .716 .072(PAG. )J 450 203 :M .557 .056(All )J 467 203 :M .144 .014(of )J 479 203 :M -.108(the)A 59 215 :M (other )S 84 215 :M -.016(conditions )A 130 215 :M -.235(are )A 146 215 :M -.044(merely )A 178 215 :M -.151(necessary )A 220 215 :M .5 .05( )J 225 215 :M .161 .016(conditions. )J 274 215 :M .125 .012(That )J 297 215 :M (means )S 327 215 :M .361 .036(that )J 347 215 :M -.097(there )A 371 215 :M -.126(can )A 389 215 :M .051 .005(be )J 403 215 :M (more )S 428 215 :M .202 .02(than )J 451 215 :M .047 .005(one )J 471 215 :M (PAG)S 59 227 :M .029 .003(representing a given set )J f0_10 sf (G)S f1_10 sf .028 .003(; two such PAGs have the same adjacencies, but one )J 378 227 :M .218 .022(may )J 399 227 :M .039 .004(contain )J 432 227 :M .056 .006(a )J 440 227 :M -.126A 457 227 :M -.142(endpoint)A 59 239 :M -.185(where )A 87 239 :M .218 .022(the )J 104 239 :M (other )S 129 239 :M .098 .01(contains )J 167 239 :M .056 .006(a )J 176 239 :M S f5_10 sf (-)S f1_10 sf .05 .005J 195 239 :M .144 .014(or )J 208 239 :M .351 .035J 223 239 :M .056 .006J 232 239 :M (endpoint. )S 274 239 :M -.163(There )A 301 239 :M -.235(are )A 317 239 :M .438 .044(PAGs )J 346 239 :M -.052(for )A 362 239 :M f0_10 sf .37(Equiv)A f1_10 sf .241<28>A f2_10 sf .523(G)A f1_10 sf .241<28>A f0_10 sf .563(O)A f1_10 sf .181(,)A f0_10 sf .181 .018( )J 420 239 :M .074(L)A f1_10 sf .084 .008(\)\) )J 438 239 :M .517 .052(with )J 462 239 :M -.088(enough)A 59 251 :M .221 .022(orientation information to determine whether or not each DAG in )J f0_10 sf .07(Equiv)A f1_10 sf <28>S f2_10 sf .099(G)A f1_10 sf <28>S f0_10 sf .107(O)A f1_10 sf (,)S f0_10 sf .105 .01( L)J f1_10 sf .165 .016(\)\) entails that )J f0_10 sf .099(A)A f1_10 sf .107 .011( and )J f0_10 sf .092(B)A f1_10 sf ( )S 480 251 :M -.602(are)A 59 263 :M -.216(independent )A 109 263 :M -.045(conditional )A 157 263 :M .417 .042(on )J 171 263 :M .047 .005(any )J 189 263 :M .315 .032(subset )J 218 263 :M -.242(included )A 254 263 :M .601 .06(in )J 266 263 :M f0_10 sf .79(O)A f1_10 sf .31<5C28>A f0_10 sf .897 .09(A )J 293 263 :M f5_10 sf .62A f1_10 sf .202 .02( )J 305 263 :M f0_10 sf .316(B)A f1_10 sf .34 .034(\); )J 322 263 :M -.079(we )A 337 263 :M .676 .068(will )J 357 263 :M .133 .013(say )J 374 263 :M .361 .036(that )J 393 263 :M .047 .005(any )J 411 263 :M .123 .012(such )J 433 263 :M .387 .039(PAG )J 458 263 :M .361 .036(that )J 478 263 :M -.164(has)A 59 275 :M .038 .004(enough )J 92 275 :M .133 .013(orientations )J 143 275 :M .601 .06(to )J 155 275 :M -.25(do )A 168 275 :M .753 .075(this )J 187 275 :M .694 .069(is )J 198 275 :M -.116(\322weakly )A 234 275 :M -.065(complete\323 )A 278 275 :M -.052(for )A 293 275 :M f0_10 sf .37(Equiv)A f1_10 sf .241<28>A f2_10 sf .523(G)A f1_10 sf .241<28>A f0_10 sf .563(O)A f1_10 sf .181(,)A f0_10 sf .181 .018( )J 350 275 :M .246(L)A f1_10 sf .33 .033(\)\). )J 370 275 :M -.229(\(Weak )A 399 275 :M -.031(completeness )A 456 275 :M -.207(does )A 478 275 :M f2_10 sf .111(not)A 59 287 :M f1_10 sf .098 .01(entail that every ancestor relation common to every member of )J f0_10 sf .032(Equiv)A f1_10 sf <28>S f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf .047 .005( L)J f1_10 sf .098 .01(\)\) is explicitly represented )J 483 287 :M .222(in)A 59 299 :M .254 .025(the PAG.\))J 59 315 :M .359 .036(Thus )J 83 315 :M .056 .006(a )J 91 315 :M .387 .039(PAG )J 115 315 :M -.126(can )A 132 315 :M .051 .005(be )J 145 315 :M -.207(used )A 166 315 :M .601 .06(to )J 178 315 :M -.126(represent )A 217 315 :M .515 .052(both )J 239 315 :M .218 .022(the )J 255 315 :M -.101(ancestor )A 291 315 :M .038 .004(relations )J 329 315 :M .189 .019(among )J 360 315 :M .218 .022(the )J 376 315 :M -.021(members )A 417 315 :M .144 .014(of )J 430 315 :M f0_10 sf .546(O)A f1_10 sf .175 .018( )J 443 315 :M .315 .032(common )J 483 315 :M .222(to)A 59 327 :M -.021(members )A 99 327 :M .144 .014(of )J 111 327 :M f0_10 sf .744(G)A f1_10 sf .435 .043(, )J 126 327 :M -.313(and )A 143 327 :M .218 .022(the )J 159 327 :M .303 .03(set )J 174 327 :M .144 .014(of )J 186 327 :M -.045(conditional )A 234 327 :M -.289(independence )A 289 327 :M .038 .004(relations )J 327 327 :M .189 .019(among )J 358 327 :M .218 .022(the )J 374 327 :M -.021(members )A 414 327 :M .144 .014(of )J 426 327 :M f0_10 sf .546(O)A f1_10 sf .175 .018( )J 439 327 :M .601 .06(in )J 452 327 :M f0_10 sf .744(G)A f1_10 sf .435 .043(. )J 468 327 :M .075(Some)A 59 339 :M .444 .044(PAGs \(e.g. PAG\()J f0_10 sf .114(Equiv)A f1_10 sf .074<28>A f2_10 sf .16(G)A f1_6 sf 0 2 rm .067(1)A 0 -2 rm f1_10 sf .074<28>A f0_10 sf .173(O)A f1_10 sf .056(,)A f0_10 sf .148(L)A f1_10 sf .213 .021(\)\)\) )J 205 339 :M .601 .06(in )J 217 339 :M .248 .025(Figure )J 247 339 :M .144 .014(1\) )J 259 339 :M -.126(represent )A 298 339 :M .5 .05( )J 302 339 :M .056 .006(a )J 310 339 :M .303 .03(set )J 325 339 :M .144 .014(of )J 337 339 :M -.045(conditional )A 385 339 :M -.289(independence )A 440 339 :M .038 .004(relations )J 478 339 :M .111(not)A 59 351 :M .038 .004(entailed by any DAG )J f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf .024 .002(\) where )J f0_10 sf (L)S f1_10 sf ( = )S f5_10 sf S f1_10 sf (.)S 59 367 :M .092 .009(PAGs have two distinct uses. Just as DAGs can be used )J 287 367 :M .417 .042(by )J 301 367 :M .366 .037(algorithms )J 348 367 :M .601 .06(to )J 360 367 :M -.1(perform )A 395 367 :M .047 .005(fast )J 413 367 :M -.031(conditionalizations,)A 59 379 :M .438 .044(PAGs )J 87 379 :M -.126(can )A 104 379 :M .051 .005(be )J 117 379 :M -.207(used )A 138 379 :M .601 .06(in )J 150 379 :M .056 .006(a )J 159 379 :M .43 .043(similar )J 192 379 :M .244 .024(way. )J 216 379 :M -.24(And )A 237 379 :M .753 .075(just )J 257 379 :M .517 .052(as, )J 273 379 :M .189 .019(given )J 300 379 :M .056 .006(a )J 309 379 :M -.081(causal )A 338 379 :M .055 .005(interpretation, )J 399 379 :M (DAGs )S 429 379 :M -.126(can )A 447 379 :M .051 .005(be )J 461 379 :M -.207(used )A 483 379 :M .222(to)A 59 391 :M -.057(calculate the )A 112 391 :M -.163(effects )A 141 391 :M .144 .014(of )J 153 391 :M .047 .005(any )J 171 391 :M -.187(ideal )A 193 391 :M .083 .008(intervention )J 245 391 :M .357 .036(upon )J 269 391 :M .056 .006(a )J 277 391 :M .722 .072(system, )J 312 391 :M .742 .074(PAGs, )J 343 391 :M .189 .019(given )J 369 391 :M .056 .006(a )J 377 391 :M -.081(causal )A 405 391 :M .055 .005(interpretation, )J 465 391 :M -.126(can )A 482 391 :M -.439(be)A 59 403 :M -.207(used )A 80 403 :M .601 .06(to )J 92 403 :M -.114(calculate )A 130 403 :M .218 .022(the )J 146 403 :M -.163(effects )A 175 403 :M .144 .014(of )J 187 403 :M f2_10 sf .212(some)A f1_10 sf .103 .01( )J 212 403 :M -.187(ideal )A 234 403 :M .127 .013(interventions )J 291 403 :M .357 .036(upon )J 316 403 :M .056 .006(a )J 325 403 :M .722 .072(system. )J 361 403 :M -.066(\(See )A 383 403 :M .429 .043(Spirtes )J 416 403 :M .236 .024(et )J 428 403 :M .602 .06(al. )J 443 403 :M .357 .036(1993 )J 468 403 :M -.356(where)A 59 415 :M -.046(PAGs are called POIPGs.\))A 59 431 :M -.021(While it would generally be preferable to know the true causal DAG )A f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf -.022(\) rather than a PAG representing)A 59 443 :M f0_10 sf .059(Equiv)A f1_10 sf <28>S f2_10 sf .083(G)A f1_10 sf <28>S f0_10 sf .09(O)A f1_10 sf (,)S f0_10 sf .088 .009( L)J f1_10 sf .164 .016(\)\), there are several reasons )J 233 443 :M .216 .022(why )J 254 443 :M .786 .079(it )J 264 443 :M .218 .022(may )J 285 443 :M .051 .005(be )J 298 443 :M -.135(easier )A 324 443 :M .601 .06(to )J 336 443 :M -.151(find )A 355 443 :M .056 .006(a )J 363 443 :M .387 .039(PAG )J 387 443 :M -.076(representing )A 439 443 :M f0_10 sf .235(Equiv)A f1_10 sf .153<28>A f2_10 sf .331(G)A f1_10 sf .153<28>A f0_10 sf .357(O)A f1_10 sf (,)S 59 455 :M f0_10 sf .17(L)A f1_10 sf .233 .023(\)\) than it is to find )J f2_10 sf .184(G)A f1_10 sf .085<28>A f0_10 sf .198(O)A f1_10 sf .064(,)A f0_10 sf .17(L)A f1_10 sf .32 .032(\) itself. First the space of PAGs is finite, while )J 365 455 :M .218 .022(the )J 381 455 :M -.141(space )A 406 455 :M .144 .014(of )J 418 455 :M (DAGs )S 447 455 :M .517 .052(with )J 469 455 :M -.042(latent)A 59 467 :M -.065(variables )A 98 467 :M .694 .069(is )J 109 467 :M .59 .059(infinite. )J 145 467 :M -.062(Second, )A 180 467 :M -.052(for )A 195 467 :M .056 .006(a )J 203 467 :M -.037(variety )A 234 467 :M .144 .014(of )J 246 467 :M -.081(scores )A 274 467 :M -.052(for )A 289 467 :M -.064(models )A 321 467 :M -.031(\(such )A 346 467 :M .144 .014(as )J 358 467 :M .237 .024(BIC, )J 382 467 :M (posterior )S 422 467 :M .509 .051(probability, )J 474 467 :M -.121(etc.\))A 59 479 :M -.048(there may be many different DAGs which receive the same score, )A 323 479 :M .555 .056(but )J 340 479 :M -.126(represent )A 379 479 :M -.213(different )A 415 479 :M -.081(causal )A 443 479 :M -.019(theories )A 478 479 :M -.719(and)A 59 491 :M -.081(make different predictions about the effects )A 233 491 :M .144 .014(of )J 245 491 :M .127 .013(interventions )J 301 491 :M .357 .036(upon )J 325 491 :M .056 .006(a )J 333 491 :M .722 .072(system. )J 368 491 :M (The )S 387 491 :M -.289(data )A 406 491 :M -.031(alone )A 431 491 :M -.207(does )A 452 491 :M .555 .056(not )J 469 491 :M -.054(allow)A 59 503 :M .047 .005(one )J 77 503 :M .601 .06(to )J 89 503 :M .289 .029(distinguish )J 137 503 :M -.116(between )A 173 503 :M (these )S 197 503 :M .068 .007(models, )J 232 503 :M .509 .051(so )J 245 503 :M -.094(even )A 267 503 :M .517 .052(with )J 289 503 :M .363 .036(population )J 336 503 :M -.131(data, )A 358 503 :M .047 .005(one )J 376 503 :M -.026(cannot )A 406 503 :M .051 .005(be )J 419 503 :M -.039(sure )A 439 503 :M .043 .004(which )J 467 503 :M .694 .069(is )J 479 503 :M -.108(the)A 59 515 :M -.124(correct causal )A 116 515 :M (model. )S 147 515 :M -.049(Nevertheless, )A 204 515 :M -.052(for )A 219 515 :M .281 .028(some )J 244 515 :M .281 .028(\(but )J 264 515 :M .555 .056(not )J 281 515 :M .126 .013(all\) )J 298 515 :M -.204(equivalence )A 347 515 :M -.037(classes )A 378 515 :M .144 .014(of )J 390 515 :M -.081(causal )A 418 515 :M .068 .007(models, )J 453 515 :M -.313(and )A 470 515 :M -.035(some)A 59 527 :M .281 .028(\(but )J 79 527 :M .555 .056(not )J 96 527 :M .126 .013(all\) )J 113 527 :M -.187(ideal )A 136 527 :M .33 .033(interventions, )J 196 527 :M .786 .079(it )J 207 527 :M .694 .069(is )J 219 527 :M .404 .04(possible )J 257 527 :M .601 .06(to )J 270 527 :M .133 .013(use )J 288 527 :M .056 .006(a )J 297 527 :M .387 .039(PAG )J 322 527 :M .601 .06(to )J 335 527 :M .242 .024(consistenly )J 385 527 :M .101 .01(estimate )J 423 527 :M .218 .022(the )J 440 527 :M -.208(effect )A 466 527 :M .144 .014(of )J 479 527 :M -.108(the)A 59 539 :M -.009(intervention, even without knowing which causal models represented by the PAG is the correct model. Note)A 59 551 :M .395 .039(that this strategy is not )J 156 551 :M .042 .004(useful )J 184 551 :M .601 .06(in )J 196 551 :M -.017(instances )A 236 551 :M -.185(where )A 263 551 :M -.141(every )A 288 551 :M (pair )S 307 551 :M .144 .014(of )J 319 551 :M -.226(measured )A 359 551 :M -.065(variables )A 398 551 :M .133 .013(has )J 415 551 :M .281 .028(some )J 440 551 :M .315 .032(strong )J 469 551 :M -.042(latent)A 59 563 :M .261 .026(common cause; in that case the PAG that represents )J f0_10 sf .089(Equiv)A f1_10 sf .058<28>A f2_10 sf .126(G)A f1_10 sf .058<28>A f0_10 sf .136(O)A f1_10 sf (,)S f0_10 sf ( )S 327 563 :M .074(L)A f1_10 sf .084 .008(\)\) )J 344 563 :M .694 .069(is )J 355 563 :M .036 .004(completely )J 403 563 :M -.153(connected, )A 448 563 :M -.313(and )A 465 563 :M -.131(cannot)A 59 575 :M -.015(be used to predict the effects of any ideal interventions on the system.)A 59 591 :M .236 .024(Is )J 70 591 :M .786 .079(it )J 80 591 :M .404 .04(possible )J 117 591 :M .601 .06(to )J 129 591 :M -.151(find )A 148 591 :M .056 .006(a )J 156 591 :M .387 .039(PAG )J 180 591 :M .047 .005(from )J 203 591 :M -.289(data )A 222 591 :M -.313(and )A 239 591 :M -.17(background )A 288 591 :M -.181(knowledge? )A 339 591 :M .5 .05( )J 344 591 :M (The )S 364 591 :M .726 .073(FCI )J 385 591 :M .56 .056(algorithm, )J 432 591 :M -.253(under )A 458 591 :M .056 .006(a )J 467 591 :M .303 .03(set )J 483 591 :M -.328(of)A 59 603 :M .504 .05(assumptions )J 114 603 :M -.312(described )A 154 603 :M .429 .043(Spirtes )J 187 603 :M .5 .05( )J 192 603 :M .236 .024(et )J 204 603 :M .602 .06(al. )J 219 603 :M .667 .067(1993, )J 247 603 :M .694 .069(is )J 259 603 :M -.236(guaranteed )A 305 603 :M .601 .06(in )J 318 603 :M .218 .022(the )J 335 603 :M -.097(large )A 359 603 :M .111 .011(sample )J 392 603 :M 1.072 .107(limit )J 418 603 :M .601 .06(to )J 432 603 :M -.151(find )A 453 603 :M .056 .006(a )J 463 603 :M -.175(weakly)A 59 615 :M -.019(complete )A 100 615 :M -.178(correct )A 131 615 :M .5 .05( )J 136 615 :M .387 .039(PAG )J 161 615 :M -.052(for )A 177 615 :M .056 .006(a )J 186 615 :M .189 .019(given )J 213 615 :M .387 .039(distribution. )J 267 615 :M .328 .033(It )J 278 615 :M .202 .02(uses )J 300 615 :M .056 .006(a )J 310 615 :M -.044(series )A 338 615 :M .144 .014(of )J 352 615 :M -.045(conditional )A 402 615 :M -.289(independence )A 459 615 :M .484 .048(tests )J 483 615 :M .222(to)A 59 627 :M .091 .009(construct a PAG that represents a given distribution. The algorithm is exponential in the number of vertices)J 59 639 :M .421 .042(in the PAG in )J 120 639 :M .218 .022(the )J 136 639 :M .19 .019(worst )J 162 639 :M -.176(case )A 182 639 :M -.052(\(as )A 197 639 :M .694 .069(is )J 208 639 :M .047 .005(any )J 226 639 :M .327 .033(algorithm )J 269 639 :M -.253(based )A 294 639 :M .357 .036(upon )J 318 639 :M -.045(conditional )A 366 639 :M -.289(independence )A 421 639 :M .529 .053(tests.\) )J 449 639 :M .5 .05( )J 453 639 :M -.163(However,)A 59 651 :M -.018(the large sample reliability does not guarantee )A 246 651 :M .298 .03(reliability )J 289 651 :M .417 .042(on )J 303 651 :M -.016(realistic )A 338 651 :M .111 .011(sample )J 370 651 :M .354 .035(sizes, )J 396 651 :M -.313(and )A 413 651 :M .328 .033(if )J 423 651 :M .218 .022(the )J 439 651 :M -.097(power )A 467 651 :M .144 .014(of )J 479 651 :M -.108(the)A 59 663 :M .025 .003(conditional independence tests is low, the results of the tests are not )J 334 663 :M .036 .004(compatible )J 382 663 :M .517 .052(with )J 404 663 :M .047 .005(any )J 422 663 :M .385 .038(single )J 450 663 :M .716 .072(PAG. )J 477 663 :M .057(For)A 59 675 :M -.02(these reasons, it would be desirable to have a search that was not based upon conditional )A 415 675 :M -.289(independence )A 470 675 :M .145(tests,)A endp %%Page: 4 4 %%BeginPageSetup initializepage (peter; page: 4 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 59 51 :M f1_10 sf -.034(or could be used to supplement an algorithm based upon conditional independence tests by )A 423 51 :M .555 .056(using )J 449 51 :M .218 .022(the )J 465 51 :M .089(output)A 59 63 :M .168 .017(of the FCI algorithm as a starting point for a search.)J 59 79 :M .022 .002(Recently, a number of algorithms for searching for DAGs without latent variables have )J 412 79 :M -.094(been )A 434 79 :M -.288(developed )A 476 79 :M (that)S 59 91 :M -.25(do )A 72 91 :M .555 .056(not )J 89 91 :M (rely )S 108 91 :M .417 .042(on )J 122 91 :M -.045(conditional )A 170 91 :M -.289(independence )A 225 91 :M .767 .077(tests. )J 250 91 :M -.023(\(Chickering )A 301 91 :M .236 .024(et )J 312 91 :M .602 .06(al. )J 327 91 :M .667 .067(1995, )J 355 91 :M .429 .043(Spirtes )J 388 91 :M -.313(and )A 406 91 :M -.066(Meek )A 433 91 :M .115 .011(1995\) )J 461 91 :M -.196(Instead,)A 59 103 :M -.01(these are heuristic searches that attempt to maximize a score. We )A 322 103 :M .676 .068(will )J 342 103 :M -.226(describe )A 377 103 :M -.176(here )A 397 103 :M .056 .006(a )J 405 103 :M .038 .004(heuristic )J 443 103 :M .387 .039(PAG )J 467 103 :M -.306(search)A 59 115 :M .197 .02(that attempts to find a PAG with the highest score. One problem with this approach is )J 410 115 :M .361 .036(that )J 429 115 :M -.163(because )A 463 115 :M .056 .006(a )J 471 115 :M (PAG)S 59 127 :M -.103(represents )A 102 127 :M .056 .006(a )J 110 127 :M .303 .03(set )J 125 127 :M .144 .014(of )J 137 127 :M -.053(DAG )A 162 127 :M -.064(models )A 194 127 :M .043 .004(which )J 222 127 :M .218 .022(may )J 244 127 :M -.194(receive )A 276 127 :M -.213(different )A 313 127 :M -.081(scores )A 342 127 :M -.084(\(either )A 372 127 :M -.187(Bayes )A 400 127 :M -.023(Information )A 452 127 :M .045(Criterion,)A 59 139 :M .058 .006(posterior probability, etc.\) a PAG cannot be assigned a score directly. In the next section we will show )J 474 139 :M -.11(how)A 59 151 :M .109 .011(to indirectly assign a score to a PAG.)J 59 174 :M f0_10 sf (I)S 63 174 :M (V)S 71 174 :M (.)S 75 174 :M 17.5 1.75( )J 95 174 :M 3.102 .31(Mixed Ancestral Graphs \(MAGs\))J 59 192 :M f1_10 sf .076 .008(A MAG \(or )J 110 192 :M -.099(mixed )A 138 192 :M -.114(ancestral )A 176 192 :M -.099(graph\) )A 205 192 :M .694 .069(is )J 216 192 :M .056 .006(a )J 224 192 :M .036 .004(completely )J 272 192 :M -.158(oriented )A 307 192 :M .387 .039(PAG )J 331 192 :M -.052(for )A 346 192 :M .056 .006(a )J 354 192 :M .303 .03(set )J 369 192 :M .144 .014(of )J 381 192 :M -.026(graphs )A 411 192 :M .043 .004(which )J 439 192 :M .465 .047(consists )J 475 192 :M .144 .014(of )J 487 192 :M (a)S 59 204 :M -.057(single directed acyclic graph )A f2_10 sf -.105(G)A f1_10 sf <28>S f0_10 sf -.113(O)A f1_10 sf (,)S f0_10 sf -.097(L)A f1_10 sf -.063(\). \(By )A 228 204 :M .036 .004(completely )J 276 204 :M -.158(oriented )A 311 204 :M -.079(we )A 326 204 :M -.039(mean )A 351 204 :M .361 .036(that )J 370 204 :M -.097(there )A 393 204 :M -.235(are )A 408 204 :M .417 .042(no )J 422 204 :M -.126A 439 204 :M -.043(endpoints )A 481 204 :M (on)S 59 216 :M -.007(any edge\). Some examples of MAGs are shown in)A 59 232 :M .215 .021(Figure )J f0_10 sf .064(1)A f1_10 sf .146 .015(, where )J f0_10 sf .099(O)A f1_10 sf .231 .023( = {A,B,C,D}.)J 59 248 :M -.014(MAGs have the following useful features:)A 95 264 :M f5_10 sf S 100 264 :M 10.5 1.05( )J 113 264 :M f1_10 sf .277 .028(DAG )J f2_10 sf .116(G)A f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf .173 .017( in Figure 1 is an example of )J 268 264 :M .056 .006(a )J 276 264 :M -.053(DAG )A 301 264 :M .123 .012(such )J 323 264 :M .361 .036(that )J 342 264 :M .144 .014(as )J 354 264 :M .218 .022(the )J 370 264 :M .111 .011(sample )J 402 264 :M (size )S 421 264 :M -.126(increases )A 460 264 :M .074(without)A 95 276 :M -.041(limit, the difference between the Bayes Information Criterion \(BIC\) of MAG\()A f2_10 sf -.072(G)A f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf (,)S f0_10 sf -.077(O)A f1_10 sf -.045(\) and )A 447 276 :M .218 .022(the )J 463 276 :M -.056(BIC )A 483 276 :M -.328(of)A 95 288 :M .047 .005(any )J 113 288 :M -.053(DAG )A 138 288 :M f2_10 sf <47D5>S f1_10 sf ( )S 152 288 :M .361 .036(that )J 171 288 :M .098 .01(contains )J 208 288 :M .515 .052(only )J 230 288 :M -.065(variables )A 269 288 :M .601 .06(in )J 281 288 :M f0_10 sf .546(O)A f1_10 sf .175 .018( )J 293 288 :M -.126(increases )A 332 288 :M .556 .056(without )J 367 288 :M 1.072 .107(limit )J 391 288 :M .523 .052(almost )J 422 288 :M .333 .033(surely. )J 454 288 :M -.207(Hence )A 483 288 :M .222(in)A 95 300 :M .11 .011(some cases a maximum likelihood estimate of the )J 299 300 :M .132 .013(MAG )J 326 300 :M -.136(parameters )A 372 300 :M .694 .069(is )J 383 300 :M .056 .006(a )J 391 300 :M -.044(better )A 417 300 :M .154 .015(estimator )J 458 300 :M .144 .014(of )J 470 300 :M -.035(some)A 95 312 :M .009 .001(of the population parameters than the maximum likelihood estimate of any DAG parameters.)J 95 328 :M f5_10 sf S 100 328 :M 10.5 1.05( )J 113 328 :M f1_10 sf .144 .014(In )J 125 328 :M .218 .022(the )J 141 328 :M -.097(large )A 164 328 :M .111 .011(sample )J 197 328 :M 1.318 .132(limit, )J 225 328 :M -.052(for )A 241 328 :M -.011(multi-variate )A 297 328 :M .111 .011(normal )J 330 328 :M .144 .014(or )J 343 328 :M -.199(discrete )A 377 328 :M .418 .042(distributions, )J 435 328 :M .047 .005(any )J 454 328 :M .042(\(possibly)A 95 340 :M .013 .001(latent variable\) DAG with a maximum BIC score is represented by the MAG with the )J 442 340 :M .362 .036(highest )J 475 340 :M -.334(BIC)A 95 352 :M .096 .01(score among all MAGs.)J 95 368 :M f5_10 sf S 100 368 :M 10.5 1.05( )J 113 368 :M f1_10 sf -.007(There is a three place graphical relation among disjoint sets )A 354 368 :M .144 .014(of )J 366 368 :M -.074(vertices )A 400 368 :M .243<28>A f0_10 sf .527(A)A f1_10 sf .183 .018( )J 415 368 :M .694 .069(is )J 426 368 :M -.325(d-separated )A 472 368 :M -.145(from)A 95 380 :M .203 .02(B given )J f0_10 sf .121(C)A f1_10 sf .208 .021(\) which holds if and only if the MAG entails that )J f0_10 sf .121(A)A f1_10 sf ( )S 349 380 :M .694 .069(is )J 360 380 :M -.216(independent )A 410 380 :M .144 .014(of )J 422 380 :M f0_10 sf .604(B)A f1_10 sf .226 .023( )J 433 380 :M -.045(conditional )A 481 380 :M (on)S 95 392 :M f0_10 sf 1.052(C)A f1_10 sf .662 .066(. )J 111 392 :M -.095(D-separation )A 166 392 :M .601 .06(in )J 179 392 :M .202 .02(MAGs )J 211 392 :M .694 .069(is )J 223 392 :M .056 .006(a )J 232 392 :M .523 .052(simple )J 264 392 :M .093 .009(extension )J 307 392 :M .144 .014(of )J 320 392 :M -.037(Pearl\325s )A 352 392 :M -.16(d-separation )A 404 392 :M (relation )S 439 392 :M -.062(\(Pearl )A 468 392 :M -.082(1988\))A 95 404 :M -.164(defined over DAGs.)A 59 420 :M .072 .007(If the graph )J f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf .088 .009(\) that a MAG represents is included in the PAG that represents )J f0_10 sf .032(Equiv)A f1_10 sf <28>S f2_10 sf (G)S f1_10 sf <28>S f0_10 sf (O)S f1_10 sf (,)S f0_10 sf (L)S f1_10 sf .091 .009(\)\), then we)J 59 432 :M .229 .023(say that the )J 109 432 :M .387 .039(PAG )J 133 432 :M -.103(represents )A 176 432 :M .218 .022(the )J 192 432 :M .48 .048(MAG. )J 222 432 :M .472 .047(For )J 240 432 :M -.141(every )A 265 432 :M .716 .072(PAG, )J 292 432 :M -.097(there )A 315 432 :M .694 .069(is )J 326 432 :M .281 .028(some )J 351 432 :M .132 .013(MAG )J 378 432 :M .361 .036(that )J 397 432 :M .786 .079(it )J 407 432 :M -.048(represents, )A 453 432 :M -.313(and )A 470 432 :M -.301(every)A 59 444 :M -.056(MAG represented by a PAG receives the same )A 247 444 :M -.056(BIC )A 267 444 :M -.016(score. )A 294 444 :M .359 .036(Thus )J 318 444 :M .056 .006(a )J 326 444 :M .387 .039(PAG )J 350 444 :M -.126(can )A 367 444 :M .051 .005(be )J 380 444 :M -.117(assigned )A 417 444 :M .056 .006(a )J 425 444 :M -.119(score )A 449 444 :M .417 .042(by )J 463 444 :M -.147(finding)A 59 456 :M .144 .014(some MAG that it represents, scoring the MAG, and assigning that score to )J 367 456 :M .218 .022(the )J 383 456 :M .716 .072(PAG. )J 410 456 :M .328 .033(It )J 420 456 :M .694 .069(is )J 431 456 :M .404 .04(possible )J 468 456 :M .361 .036(that )J 487 456 :M (a)S 59 468 :M -.03(PAG represents some non-MAG model that receives a )A 279 468 :M (higher )S 308 468 :M -.056(BIC )A 328 468 :M -.119(score )A 352 468 :M .202 .02(than )J 373 468 :M .047 .005(any )J 391 468 :M .132 .013(MAG )J 418 468 :M -.234(represented )A 465 468 :M .417 .042(by )J 479 468 :M -.108(the)A 59 480 :M .167 .017(PAG. However, assigning a MAG )J 201 480 :M -.119(score )A 225 480 :M .601 .06(to )J 237 480 :M .056 .006(a )J 245 480 :M .387 .039(PAG )J 269 480 :M .361 .036(that )J 288 480 :M -.103(represents )A 331 480 :M .786 .079(it )J 341 480 :M .133 .013(has )J 358 480 :M .218 .022(the )J 374 480 :M .325 .033(following )J 417 480 :M -.177(desirable )A 455 480 :M -.046(property.)A 59 492 :M .258 .026(For any distribution )J f2_10 sf .098(P)A f1_10 sf .054<28>A f0_10 sf .125(O)A f1_10 sf .185 .018(\), if there is some DAG )J f2_10 sf .116(G)A f1_10 sf .2 .02( that contains )J f0_10 sf .125(O)A f1_10 sf .168 .017(, such that for )J 389 492 :M .047 .005(any )J 407 492 :M -.097(three )A 430 492 :M .276 .028(disjoint )J 464 492 :M .361 .036(sets )J 483 492 :M -.328(of)A 59 504 :M .583 .058(variables )J f0_10 sf .218(X)A f1_10 sf .126 .013(, )J f0_10 sf .218(Y)A f1_10 sf .126 .013(, )J f0_10 sf .202(Z)A f1_10 sf .069 .007( )J f5_10 sf .215A f1_10 sf .069 .007( )J f0_10 sf .235(O)A f1_10 sf .126 .013(, )J f0_10 sf .218(X)A f1_10 sf .378 .038( is independent of )J f0_10 sf .218(Y)A f1_10 sf .305 .03( given )J f0_10 sf .202(Z)A f1_10 sf .265 .026( if and only if )J 342 504 :M f0_10 sf .951(X)A f1_10 sf .329 .033( )J 354 504 :M .694 .069(is )J 365 504 :M -.325(d-separated )A 411 504 :M .047 .005(from )J 434 504 :M f0_10 sf .951(Y)A f1_10 sf .329 .033( )J 446 504 :M .189 .019(given )J 472 504 :M f0_10 sf .604(Z)A f1_10 sf .226 .023( )J 483 504 :M .222(in)A 59 516 :M f2_10 sf .368(G)A f1_10 sf .467 .047(, then )J f0_10 sf .312(P)A f1_10 sf .17<28>A f0_10 sf .397(O)A f1_10 sf .432 .043(\) is said to be )J f0_10 sf .202(faithful)A f1_10 sf .272 .027( to )J f2_10 sf .368(G)A f1_10 sf .447 .045( over )J f0_10 sf .397(O)A f1_10 sf .501 .05(. For any )J 297 516 :M -.011(multi-variate )A 352 516 :M .111 .011(normal )J 384 516 :M .178 .018(distribution )J 434 516 :M f2_10 sf .11(P)A f1_10 sf .06<28>A f0_10 sf .139(O)A f1_10 sf .124 .012(\), )J 461 516 :M .328 .033(if )J 471 516 :M f2_10 sf -.161(P)A f1_10 sf -.088<28>A f0_10 sf -.205(O)A f1_10 sf <29>S 59 528 :M .32 .032(is faithful to some DAG )J f2_10 sf .172(G)A f1_10 sf .209 .021( over )J f0_10 sf .186(O)A f1_10 sf .214 .021(, then in )J 236 528 :M .218 .022(the )J 252 528 :M -.097(large )A 275 528 :M .111 .011(sample )J 307 528 :M 1.072 .107(limit )J 331 528 :M .218 .022(the )J 347 528 :M .387 .039(PAG )J 371 528 :M .361 .036(that )J 390 528 :M -.103(represents )A 433 528 :M f2_10 sf .209(G)A f1_10 sf .072 .007( )J 444 528 :M -.156(receives )A 479 528 :M -.108(the)A 59 540 :M .153 .015(highest BIC score among all PAGs.)J 206 540 :M .476 .048( )J 59 556 :M .255 .026(A )J 71 556 :M .132 .013(MAG )J 99 556 :M -.126(can )A 117 556 :M .281 .028(also )J 138 556 :M .051 .005(be )J 152 556 :M -.281(considered )A 197 556 :M .056 .006(a )J 206 556 :M -.081(representation )A 266 556 :M .144 .014(of )J 279 556 :M .056 .006(a )J 288 556 :M .303 .03(set )J 304 556 :M .144 .014(of )J 317 556 :M -.045(conditional )A 367 556 :M -.289(independence )A 424 556 :M .038 .004(relations )J 464 556 :M -.054(among)A 59 568 :M (variables in )S f0_10 sf (O)S f1_10 sf .012 .001( \(which in some cases cannot be represented by any DAG containing just variables in )J 461 568 :M f0_10 sf .562(O)A f1_10 sf .347 .035(; )J 476 568 :M .187(e.g.)A 59 580 :M .077(MAG\()A f2_10 sf .084(G)A f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf <28>S f0_10 sf .09(O)A f1_10 sf (,)S f0_10 sf .078(L)A f1_10 sf .163 .016(\)\) in Figure 1.\) A MAG imposes no restrictions on the set of distributions it represents other)J 59 592 :M .202 .02(than )J 80 592 :M .218 .022(the )J 96 592 :M -.045(conditional )A 144 592 :M -.289(independence )A 199 592 :M .038 .004(relations )J 237 592 :M .361 .036(that )J 256 592 :M .786 .079(it )J 266 592 :M .499 .05(entails. )J 299 592 :M -.094(\(The )A 321 592 :M .044 .004(class )J 344 592 :M .144 .014(of )J 356 592 :M .202 .02(MAGs )J 387 592 :M .694 .069(is )J 398 592 :M -.037(neither )A 430 592 :M .056 .006(a )J 439 592 :M .315 .032(subset )J 469 592 :M .133 .013(nor )J 487 592 :M (a)S 59 604 :M -.033(superset )A 95 604 :M .144 .014(of )J 107 604 :M (other )S 131 604 :M -.068(generalizations )A 194 604 :M .144 .014(of )J 207 604 :M (DAGs )S 237 604 :M .123 .012(such )J 260 604 :M .144 .014(as )J 273 604 :M -.031(chain )A 299 604 :M .203 .02(graphs, )J 333 604 :M -.062(cyclic )A 361 604 :M -.337(directed )A 395 604 :M .203 .02(graphs, )J 429 604 :M .144 .014(or )J 442 604 :M -.062(cyclic )A 470 604 :M -.164(chain)A 59 616 :M -.069(graphs.\))A 59 632 :M f4_10 sf (A)S 67 632 :M (.)S 71 632 :M 21.5 2.15( )J 95 632 :M 5.538 .554(Parameterizing MAGs)J 59 648 :M f1_10 sf -.078(We will describe )A 129 648 :M .216 .022(how )J 150 648 :M .056 .006(a )J 158 648 :M -.105(parameterization )A 227 648 :M .144 .014(of )J 239 648 :M .056 .006(a )J 247 648 :M .132 .013(MAG )J 274 648 :M .601 .06(in )J 286 648 :M .218 .022(the )J 302 648 :M -.011(multi-variate )A 357 648 :M .111 .011(normal )J 389 648 :M -.176(case )A 409 648 :M .694 .069(is )J 420 648 :M .051 .005(an )J 433 648 :M .093 .009(extension )J 475 648 :M .144 .014(of )J 487 648 :M (a)S 59 660 :M -.105(parameterization )A 130 660 :M .144 .014(of )J 144 660 :M .056 .006(a )J 154 660 :M -.053(DAG )A 181 660 :M -.131(corresponding )A 243 660 :M .601 .06(to )J 258 660 :M .056 .006(a )J 269 660 :M -.063(\322structural )A 317 660 :M -.117(equation )A 357 660 :M -.062(model\323. )A 395 660 :M .5 .05( )J 402 660 :M -.092(\(Parameterization )A 478 660 :M -.719(and)A 59 672 :M -.027(estimation of parameters in the case of discrete variables is somewhat more difficult.\))A endp %%Page: 5 5 %%BeginPageSetup initializepage (peter; page: 5 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 59 51 :M f1_10 sf -.044(The variables in a linear structural equation model \(SEM\) can be divided into )A 369 51 :M .387 .039(two )J 388 51 :M .67 .067(sets, )J 410 51 :M .218 .022(the )J 426 51 :M -.227(\322error )A 452 51 :M -.17(variables\323)A 59 63 :M .144 .014(or )J 71 63 :M -.227(\322error )A 97 63 :M .206 .021(terms,\323 )J 130 63 :M -.313(and )A 147 63 :M .218 .022(the )J 163 63 :M .242 .024(substantive )J 212 63 :M -.009(variables. )A 254 63 :M -.072(Corresponding )A 316 63 :M .601 .06(to )J 328 63 :M -.204(each )A 349 63 :M .242 .024(substantive )J 399 63 :M -.087(variable )A 435 63 :M .427(X)A f1_6 sf 0 2 rm .17 .017(i )J 0 -2 rm 448 63 :M f1_10 sf .694 .069(is )J 460 63 :M .056 .006(a )J 469 63 :M -.152(linear)A 59 75 :M (equation with X)S f1_6 sf 0 2 rm (i)S 0 -2 rm f1_10 sf -.003( on the left hand side of the equation, )A 277 75 :M -.313(and )A 294 75 :M .218 .022(the )J 310 75 :M -.21(direct )A 335 75 :M -.099(causes )A 364 75 :M .144 .014(of )J 376 75 :M .389(X)A f1_6 sf 0 2 rm .09(i)A 0 -2 rm f1_10 sf .135 .013( )J 389 75 :M .594 .059(plus )J 410 75 :M .218 .022(the )J 426 75 :M -.184(error )A 448 75 :M .126 .013(term )J 470 75 :M f5_10 sf .655(e)A f8_6 sf 0 2 rm .27(i)A 0 -2 rm f1_10 sf .373 .037( )J 481 75 :M (on)S 59 87 :M -.011(the right hand side of the equation. Since we )A 240 87 :M -.094(have )A 262 87 :M .417 .042(no )J 276 87 :M .04 .004(interest )J 309 87 :M .601 .06(in )J 321 87 :M .266 .027(first )J 341 87 :M .743 .074(moments, )J 385 87 :M .556 .056(without )J 420 87 :M .674 .067(loss )J 440 87 :M .144 .014(of )J 452 87 :M -.109(generality)A 59 99 :M -.055(each variable can be expressed as a deviation from its mean.)A 59 115 :M -.02(Consider, for )A 115 115 :M .071 .007(example, )J 155 115 :M .387 .039(two )J 174 115 :M .753 .075(SEMs )J 203 115 :M f2_10 sf .714(S)A f1_6 sf 0 2 rm .429(1)A 0 -2 rm f1_10 sf .357 .036( )J 216 115 :M -.313(and )A 233 115 :M f2_10 sf .714(S)A f1_6 sf 0 2 rm .429(2)A 0 -2 rm f1_10 sf .357 .036( )J 246 115 :M -.067(over )A 267 115 :M f0_10 sf .951(X)A f1_10 sf .329 .033( )J 279 115 :M -.14(= )A 288 115 :M ({X)S f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf (, )S 309 115 :M .37(X)A f1_6 sf 0 2 rm .154(2)A 0 -2 rm f1_10 sf .233 .023(, )J 326 115 :M (X)S f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf (}, )S 347 115 :M -.185(where )A 374 115 :M .601 .06(in )J 386 115 :M .515 .052(both )J 408 115 :M .753 .075(SEMs )J 437 115 :M .159(X)A f1_6 sf 0 2 rm .066(1)A 0 -2 rm f1_10 sf .055 .006( )J 451 115 :M .694 .069(is )J 462 115 :M .056 .006(a )J 470 115 :M -.352(direct)A 59 127 :M .203 .02(cause of X)J f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf .198 .02(. The structural equations in Figure 2 are common to both)J f2_10 sf .089 .009( S)J f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf .111 .011( and )J f2_10 sf .071(S)A f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf (.)S 260 143 :M .351(X)A f8_6 sf 0 2 rm .198 .02(1 )J 0 -2 rm f8_10 sf .358 .036(= )J f5_10 sf .213(e)A f8_6 sf 0 2 rm (1)S 0 -2 rm 240 159 :M f1_10 sf .383(X)A f8_6 sf 0 2 rm .173(2)A 0 -2 rm f8_10 sf .267 .027( = )J f5_10 sf .292(b)A f8_6 sf 0 2 rm .173(21)A 0 -2 rm f8_10 sf .131 .013( )J f1_10 sf .383(X)A f8_6 sf 0 2 rm .173(1)A 0 -2 rm f8_10 sf .267 .027( + )J f5_10 sf .233(e)A f8_6 sf 0 2 rm (2)S 0 -2 rm 259 175 :M f1_10 sf .317(X)A f8_6 sf 0 2 rm .143(3)A 0 -2 rm f8_10 sf .221 .022( = )J f5_10 sf .193(e)A f8_6 sf 0 2 rm (3)S 0 -2 rm 163 187 :M f9_10 sf .574 .057(Figure 2: Structural Equations for SEMs )J f10_10 sf .18(S)A f9_6 sf 0 1 rm .097(1)A 0 -1 rm f9_10 sf .273 .027( and )J f10_10 sf .18(S)A f9_6 sf 0 1 rm (2)S 0 -1 rm 59 203 :M f1_10 sf -.031(where )A f5_10 sf (b)S f1_6 sf 0 2 rm -.017(21 )A 0 -2 rm f1_10 sf -.027(is a free parameters ranging over real values, and )A f5_10 sf (e)S f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf (,)S f1_6 sf 0 2 rm ( )S 0 -2 rm f5_10 sf (e)S f1_6 sf 0 2 rm (2 )S 0 -2 rm f1_10 sf -.039(and )A 334 203 :M f5_10 sf .493(e)A f1_6 sf 0 2 rm .337(3)A 0 -2 rm f1_10 sf .281 .028( )J 346 203 :M -.235(are )A 361 203 :M -.184(error )A 383 203 :M .493 .049(terms. )J 412 203 :M .144 .014(In )J 424 203 :M -.159(addition )A 459 203 :M -.036(suppose)A 59 215 :M .133 .013(that )J f5_10 sf .05(e)A f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf (,)S f1_6 sf 0 2 rm ( )S 0 -2 rm f5_10 sf .05(e)A f1_6 sf 0 2 rm .043 .004(2 )J 0 -2 rm f1_10 sf .138 .014(and )J f5_10 sf .05(e)A f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf .155 .016( are distributed )J 186 215 :M .144 .014(as )J 198 215 :M .085 .008(multivariate )J 250 215 :M .398 .04(normal. )J 285 215 :M .144 .014(In )J 297 215 :M f2_10 sf .714(S)A f1_6 sf 0 2 rm .429(1)A 0 -2 rm f1_10 sf .357 .036( )J 310 215 :M -.079(we )A 325 215 :M .676 .068(will )J 345 215 :M .041 .004(assume )J 378 215 :M .361 .036(that )J 397 215 :M .218 .022(the )J 413 215 :M -.073(correlation )A 459 215 :M -.219(between)A 59 227 :M -.005(each pair of distinct error terms is fixed at zero. The free parameters of )A f2_10 sf (S)S f1_6 sf 0 2 rm (1 )S 0 -2 rm f1_10 sf (are )S f6_10 sf (q )S f1_10 sf (= <)S f6_10 sf (b)S f1_10 sf (, )S f0_10 sf (P)S f1_10 sf (>, where )S f6_10 sf (b )S 453 227 :M f1_10 sf .694 .069(is )J 464 227 :M .218 .022(the )J 480 227 :M -.053(set)A 59 239 :M -.004(of linear coefficients {)A f7_10 sf (b)S f1_6 sf 0 2 rm (21)S 0 -2 rm f1_10 sf ( } and )S f0_10 sf (P)S f1_10 sf -.004( is the set of variances of the error terms. We will use )A 409 229 28 16 rC 437 245 :M psb currentpoint pse 409 229 :M psb /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 896 div 512 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (S) -1 261 sh 224 /Times-Italic f1 (S) 255 359 sh 160 /Times-Roman f1 (1) 343 415 sh (1) 627 415 sh 224 /Times-Roman f1 (\() 441 359 sh (\)) 729 359 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (q) 516 359 sh end MTsave restore pse gR gS 0 0 552 730 rC 437 239 :M f1_10 sf -.012( to denote the)A 59 255 :M -.18(covariance )A 105 255 :M .249 .025(matrix )J 136 255 :M -.24(parameterized )A 194 255 :M .417 .042(by )J 209 255 :M .218 .022(the )J 226 255 :M -.081(vector )A 255 255 :M f7_10 sf .141(q)A f5_6 sf 0 2 rm .081(1)A 0 -2 rm f1_10 sf .068 .007( )J 268 255 :M -.052(for )A 284 255 :M -.099(model )A 313 255 :M f2_10 sf .769(S)A f1_6 sf 0 2 rm .462(1)A 0 -2 rm f1_10 sf .699 .07(, )J 330 255 :M -.313(and )A 349 255 :M -.04(occasionally )A 404 255 :M -.119(leave )A 430 255 :M .555 .056(out )J 449 255 :M .218 .022(the )J 467 255 :M -.249(model)A 59 267 :M .095 .009(subscript if the context makes it clear which )J 240 267 :M -.099(model )A 268 267 :M .694 .069(is )J 279 267 :M .189 .019(being )J 305 267 :M -.391(referred )A 337 267 :M .94 .094(to. )J 352 267 :M -.078(If )A 362 267 :M .388 .039(all )J 376 267 :M .218 .022(the )J 392 267 :M .044 .004(pairs )J 415 267 :M .144 .014(of )J 427 267 :M -.184(error )A 449 267 :M .192 .019(terms )J 475 267 :M .601 .06(in )J 487 267 :M (a)S 59 279 :M .652 .065(SEM )J f2_10 sf .198(S)A f1_10 sf .532 .053( are uncorrelated, we say )J f2_10 sf .198(S)A f1_10 sf .377 .038( is a SEM with )J f0_10 sf 1.148 .115(uncorrelated errors)J f1_10 sf (.)S 59 295 :M f2_10 sf .181(S)A f8_6 sf 0 2 rm .118(2)A 0 -2 rm f1_10 sf .538 .054( contains the same structural equations as )J f2_10 sf .181(S)A f8_6 sf 0 2 rm .118(1)A 0 -2 rm f1_10 sf .283 .028(, but in )J f2_10 sf .181(S)A f8_6 sf 0 2 rm .118(2)A 0 -2 rm f1_10 sf .09 .009( )J 294 295 :M -.079(we )A 309 295 :M .676 .068(will )J 329 295 :M .19 .019(allow )J 355 295 :M .218 .022(the )J 371 295 :M -.135(errors )A 397 295 :M -.116(between )A 433 295 :M .567(X)A f8_6 sf 0 2 rm .256(2)A 0 -2 rm f1_10 sf .196 .02( )J 448 295 :M -.313(and )A 465 295 :M .123(X)A f8_6 sf 0 2 rm ( )S 0 -2 rm 475 297 :M .701(3)A f1_10 sf 0 -2 rm .538 .054( )J 0 2 rm 483 295 :M .222(to)A 59 307 :M .051 .005(be )J 72 307 :M -.179(correlated, )A 116 307 :M 1.189 .119(i.e., )J 136 307 :M -.079(we )A 151 307 :M -.039(make )A 176 307 :M .218 .022(the )J 192 307 :M -.073(correlation )A 238 307 :M -.116(between )A 274 307 :M .218 .022(the )J 290 307 :M -.135(errors )A 316 307 :M .144 .014(of )J 328 307 :M .123(X)A f8_6 sf 0 2 rm ( )S 0 -2 rm 338 309 :M .701(2)A f1_10 sf 0 -2 rm .538 .054( )J 0 2 rm 346 307 :M -.313(and )A 363 307 :M .123(X)A f8_6 sf 0 2 rm ( )S 0 -2 rm 373 309 :M .701(3)A f1_10 sf 0 -2 rm .538 .054( )J 0 2 rm 381 307 :M .056 .006(a )J 389 307 :M -.258(free )A 407 307 :M -.097(parameter, )A 452 307 :M -.118(instead )A 483 307 :M -.328(of)A 59 319 :M .135 .014(fixing it at zero, as in X)J f8_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf .109 .011(. In X)J f8_6 sf 0 2 rm (2)S 0 -2 rm f1_6 sf 0 2 rm ( )S 0 -2 rm f1_10 sf .18 .018(the free parameters are )J f6_10 sf .064(q)A f1_10 sf .083 .008( = <)J f6_10 sf .068(b)A f1_10 sf .051 .005(, )J f0_10 sf .058<50D5>A f1_10 sf .159 .016(>, where )J f6_10 sf .082 .008(b )J f1_10 sf .181 .018(is the set of linear coefficients)J 59 331 :M -.323({)A f7_10 sf -.369(b)A f1_6 sf 0 2 rm -.202(21)A 0 -2 rm f1_10 sf -.491(} )A 83 331 :M -.313(and )A 101 331 :M f0_10 sf .816<50D5>A f1_10 sf .432 .043( )J 117 331 :M .694 .069(is )J 129 331 :M .218 .022(the )J 146 331 :M .303 .03(set )J 162 331 :M .144 .014(of )J 175 331 :M -.139(variances )A 216 331 :M .144 .014(of )J 229 331 :M .218 .022(the )J 246 331 :M -.184(error )A 269 331 :M .192 .019(terms )J 296 331 :M -.313(and )A 314 331 :M .218 .022(the )J 332 331 :M -.073(correlation )A 380 331 :M -.116(between )A 418 331 :M f5_10 sf .548(e)A f1_6 sf 0 2 rm .511 .051(2 )J 0 -2 rm 431 331 :M f1_10 sf -.313(and )A 450 331 :M f5_10 sf .571(e)A f1_6 sf 0 2 rm .39(3)A 0 -2 rm f1_10 sf .591 .059(. )J 467 331 :M -.078(If )A 479 331 :M -.108(the)A 59 343 :M -.058(correlations )A 109 343 :M -.116(between )A 145 343 :M .047 .005(any )J 163 343 :M .144 .014(of )J 175 343 :M .218 .022(the )J 191 343 :M -.184(error )A 213 343 :M .192 .019(terms )J 239 343 :M .601 .06(in )J 251 343 :M .056 .006(a )J 259 343 :M .726 .073(SEM )J 284 343 :M -.235(are )A 299 343 :M .555 .056(not )J 316 343 :M -.209(fixed )A 339 343 :M .236 .024(at )J 350 343 :M -.041(zero, )A 373 343 :M -.079(we )A 388 343 :M .676 .068(will )J 408 343 :M .047 .005(call )J 427 343 :M .786 .079(it )J 438 343 :M .056 .006(a )J 447 343 :M .726 .073(SEM )J 473 343 :M .075(with)A 59 355 :M f0_10 sf 2.328 .233(correlated errors)J f1_10 sf (.)S 59 371 :M -.03(It is possible to associate with each SEM with uncorrelated errors a directed graph )A 389 371 :M .361 .036(that )J 408 371 :M -.103(represents )A 451 371 :M .218 .022(the )J 467 371 :M -.197(causal)A 59 383 :M -.021(structure of the model and the form of the linear equations. )A 297 383 :M .472 .047(For )J 315 383 :M .071 .007(example, )J 355 383 :M .218 .022(the )J 371 383 :M -.337(directed )A 404 383 :M -.053(graph )A 430 383 :M -.159(associated )A 473 383 :M .075(with)A 59 395 :M .401 .04(the substantive variables in )J f2_10 sf .125(S)A f1_6 sf 0 2 rm .075(1)A 0 -2 rm f1_10 sf .188 .019( is X)J f1_6 sf 0 2 rm .075(1)A 0 -2 rm f1_10 sf .057 .006( )J f5_10 sf .246A f1_10 sf .202 .02( X)J f1_6 sf 0 2 rm .075(2)A 0 -2 rm f1_10 sf .057 .006( )J f5_10 sf .057 .006( )J f1_10 sf .18(X)A f1_6 sf 0 2 rm .075(3)A 0 -2 rm f1_10 sf .373 .037(, because X)J f1_6 sf 0 2 rm .075(1)A 0 -2 rm f1_10 sf .317 .032( is the only substantive )J 398 395 :M -.087(variable )A 433 395 :M .361 .036(that )J 452 395 :M -.099(occurs )A 481 395 :M (on)S 59 407 :M -.024(the right hand side of the equation for X)A f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf (.)S 59 423 :M -.026(It is generally accepted that correlation is to be explained by some form of causal connection. Accordingly if)A 59 435 :M f5_10 sf (e)S f1_6 sf 0 2 rm (2 )S 0 -2 rm f1_10 sf .087 .009(and )J f5_10 sf (e)S f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf .097 .01( are correlated we will assume that either )J f5_10 sf (e)S f1_6 sf 0 2 rm (2 )S 0 -2 rm f1_10 sf .121 .012(causes )J f5_10 sf (e)S f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf (, )S f5_10 sf (e)S f1_6 sf 0 2 rm (3 )S 0 -2 rm f1_10 sf .121 .012(causes )J f5_10 sf (e)S f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf .116 .012(, some latent variable causes both)J 59 447 :M f5_10 sf (e)S f1_6 sf 0 2 rm (2 )S 0 -2 rm f1_10 sf (and )S f5_10 sf (e)S f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf -.004(, or some combination of these. We represent the correlated error between )A f5_10 sf (e)S f1_6 sf 0 2 rm (2 )S 0 -2 rm 403 447 :M f1_10 sf -.313(and )A 420 447 :M f5_10 sf .493(e)A f1_6 sf 0 2 rm .337(3)A 0 -2 rm f1_10 sf .281 .028( )J 432 447 :M .417 .042(by )J 446 447 :M -.11(introducing)A 59 459 :M .079 .008(a latent variable T that is a common cause of X)J f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf .063 .006( and X)J f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf .035 .003(. If )J f0_10 sf (O)S f1_10 sf .055 .006( = {X)J f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf .03(,X)A f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf .03(,X)A f1_6 sf 0 2 rm (3)S 0 -2 rm f1_10 sf .071 .007(}, the MAG for the )J 436 459 :M -.337(directed )A 469 459 :M -.191(graph)A 59 471 :M -.159(associated )A 102 471 :M .517 .052(with )J 124 471 :M f2_10 sf .714(S)A f1_6 sf 0 2 rm .429(2)A 0 -2 rm f1_10 sf .357 .036( )J 137 471 :M .694 .069(is )J 148 471 :M .159(X)A f1_6 sf 0 2 rm .066(1)A 0 -2 rm f1_10 sf .055 .006( )J 162 471 :M f5_10 sf .504A f1_10 sf .128 .013( )J 176 471 :M .159(X)A f1_6 sf 0 2 rm .066(2)A 0 -2 rm f1_10 sf .055 .006( )J 190 471 :M f5_10 sf .073 .007J 204 471 :M f1_10 sf .37(X)A f1_6 sf 0 2 rm .154(3)A 0 -2 rm f1_10 sf .233 .023(. )J 221 471 :M (The )S 241 471 :M .35 .035(statistical )J 284 471 :M .32 .032(justification )J 337 471 :M -.052(for )A 353 471 :M .753 .075(this )J 373 471 :M .694 .069(is )J 385 471 :M -.256(provided )A 423 471 :M .601 .06(in )J 436 471 :M .429 .043(Spirtes )J 469 471 :M .236 .024(et )J 481 471 :M .142(al.)A 59 483 :M .265 .027(\(1996\). It turns out that the set of MAGs is a subset of the set of )J 324 483 :M -.126(recursive )A 363 483 :M -.026(structural )A 404 483 :M -.117(equation )A 441 483 :M -.064(models )A 473 483 :M .075(with)A 59 495 :M -.102(correlated errors. Hence, there are standard statistical packages such )A 328 495 :M .144 .014(as )J 340 495 :M .387 .039(LISREL )J 378 495 :M .144 .014(or )J 390 495 :M .472 .047(EQS )J 413 495 :M .043 .004(which )J 441 495 :M -.126(can )A 458 495 :M -.045(estimate)A 59 507 :M .13 .013(and perform statistical tests upon MAG models such as )J f2_10 sf (S)S f1_6 sf 0 2 rm (2)S 0 -2 rm f1_10 sf (.)S 59 523 :M f4_10 sf (B)S 66 523 :M (.)S 70 523 :M 22.5 2.25( )J 95 523 :M 3.344 .334(The Bayes Information Criterion \(BIC\) Score of a MAG)J 59 539 :M f1_10 sf .259 .026(As the )J 89 539 :M .111 .011(sample )J 121 539 :M (size )S 140 539 :M -.126(increases )A 179 539 :M .556 .056(without )J 214 539 :M 1.318 .132(limit, )J 241 539 :M .218 .022(the )J 257 539 :M -.187(Bayes )A 284 539 :M -.023(Information )A 335 539 :M .211 .021(Criterion )J 375 539 :M .694 .069(is )J 386 539 :M .051 .005(an )J 399 539 :M -.094(O\(1\) )A 421 539 :M .079 .008(approximation )J 483 539 :M -.328(of)A 59 551 :M .218 .022(the )J 76 551 :M (posterior )S 116 551 :M .387 .039(distribution. )J 170 551 :M .144 .014(In )J 183 551 :M .218 .022(the )J 200 551 :M -.176(case )A 221 551 :M .144 .014(of )J 234 551 :M .056 .006(a )J 243 551 :M -.011(multi-variate )A 299 551 :M .111 .011(normal )J 332 551 :M -.026(structural )A 374 551 :M -.117(equation )A 412 551 :M (model, )S 444 551 :M -.052(for )A 460 551 :M .056 .006(a )J 469 551 :M -.054(given)A 59 563 :M .03(sample,)A 107 579 :M .026(BIC\()A f2_10 sf (M)S f1_10 sf .056 .006( , sample\) = L\()J 195 569 36 16 rC 231 585 :M psb currentpoint pse 195 569 :M psb /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1152 div 512 3 -1 roll exch div scale currentpoint translate 64 -26 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (S) -1 346 sh 224 /Times-Italic f1 (M) 262 444 sh 224 /Times-Roman f1 (\() 471 444 sh (\)) 982 444 sh 160 ns (max) 672 500 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (q) 546 444 sh end MTsave restore pse gR gS 0 0 552 730 rC 231 579 :M f1_10 sf -.037(\) - ln\(samplesize * number of variables\) * df)A f1_6 sf 0 2 rm -.05(M)A 0 -2 rm f1_10 sf -.046(, where)A 95 599 :M f5_10 sf S 100 599 :M 10.5 1.05( )J 113 599 :M .05(q)A f1_6 sf 0 2 rm .033(max)A 0 -2 rm f1_10 sf .145 .014( is the maximum likelihood estimate of the parameters for model )J f2_10 sf .08(M)A f1_10 sf (,)S 95 615 :M f5_10 sf S 100 615 :M 10.5 1.05( )J 113 605 36 16 rC 149 621 :M psb currentpoint pse 113 605 :M psb /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1152 div 512 3 -1 roll exch div scale currentpoint translate 64 -26 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (S) -1 346 sh 224 /Times-Italic f1 (M) 262 444 sh 224 /Times-Roman f1 (\() 471 444 sh (\)) 982 444 sh 160 ns (max) 672 500 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (q) 546 444 sh end MTsave restore pse gR gS 0 0 552 730 rC 149 615 :M f1_10 sf .166 .017( is the covariance matrix for )J f2_10 sf .109(M)A f1_10 sf .134 .013( when )J f5_10 sf .097(Q)A f1_10 sf .192 .019( takes on its maximum likelihood value )J f5_10 sf .068(q)A f1_6 sf 0 2 rm .045(max)A 0 -2 rm f1_10 sf (,)S 95 635 :M f5_10 sf S 100 635 :M 10.5 1.05( )J 113 635 :M f1_10 sf -.436(L\()A 122 625 36 16 rC 158 641 :M psb currentpoint pse 122 625 :M psb /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1152 div 512 3 -1 roll exch div scale currentpoint translate 64 -26 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (S) -1 346 sh 224 /Times-Italic f1 (M) 262 444 sh 224 /Times-Roman f1 (\() 471 444 sh (\)) 982 444 sh 160 ns (max) 672 500 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (q) 546 444 sh end MTsave restore pse gR gS 0 0 552 730 rC 158 635 :M f1_10 sf .257 .026(\) is the likelihood ratio test statistic of )J 315 625 36 16 rC 351 641 :M psb currentpoint pse 315 625 :M psb /MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1152 div 512 3 -1 roll exch div scale currentpoint translate 64 -26 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Symbol f1 (S) -1 346 sh 224 /Times-Italic f1 (M) 262 444 sh 224 /Times-Roman f1 (\() 471 444 sh (\)) 982 444 sh 160 ns (max) 672 500 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 224 /Symbol f2 (q) 546 444 sh end MTsave restore pse gR gS 0 0 552 730 rC 351 635 :M f1_10 sf (,)S 95 655 :M f5_10 sf S 100 655 :M 10.5 1.05( )J 113 655 :M f1_10 sf -.044(df)A f1_6 sf 0 2 rm -.056(M)A 0 -2 rm f1_10 sf -.044( is the degrees of freedom of the MAG )A f2_10 sf -.088(M)A f1_10 sf (.)S 59 671 :M -.066(\(See )A 80 671 :M (Raftery, )S 116 671 :M .42 .042(1993\). )J 146 671 :M -.121(Each )A 170 671 :M .144 .014(of )J 183 671 :M (these )S 208 671 :M -.038(quantities )A 251 671 :M -.126(can )A 269 671 :M .051 .005(be )J 283 671 :M -.203(calculated )A 326 671 :M .417 .042(by )J 341 671 :M -.296(standard )A 377 671 :M .35 .035(statistical )J 420 671 :M -.143(packages )A 460 671 :M .123 .012(such )J 483 671 :M -.328(as)A 59 683 :M .425 .043(LISREL or EQS.)J endp %%Page: 6 6 %%BeginPageSetup initializepage (peter; page: 6 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 59 51 :M f4_10 sf (C)S 67 51 :M (.)S 71 51 :M 21.5 2.15( )J 95 51 :M 3.237 .324(Greedy BIC MAG Search)J 59 67 :M f1_10 sf .136 .014(A greedy search among MAGs is given as input a MAG to start with \(possibly a )J 387 67 :M .132 .013(MAG )J 414 67 :M .517 .052(with )J 436 67 :M .417 .042(no )J 450 67 :M -.156(edges\). )A 481 67 :M (At)S 59 79 :M -.204(each )A 80 79 :M .285 .028(stage, )J 107 79 :M .218 .022(the )J 123 79 :M .327 .033(algorithm )J 166 79 :M (takes )S 190 79 :M .218 .022(the )J 206 79 :M .132 .013(MAG )J 233 79 :M .555 .056(M )J 246 79 :M .786 .079(it )J 256 79 :M .133 .013(has )J 273 79 :M -.144(constructed )A 321 79 :M .594 .059(thus )J 343 79 :M -.198(far )A 358 79 :M -.313(and )A 376 79 :M -.092(calculates )A 419 79 :M .218 .022(the )J 436 79 :M -.119(score )A 461 79 :M .144 .014(of )J 474 79 :M -.438(each)A 59 91 :M -.091(MAG resulting from a one edge addition \(directed or )A 270 91 :M -.261(bi-directed\) )A 317 91 :M .601 .06(to )J 329 91 :M f2_10 sf 1.045(M)A f1_10 sf .57 .057(, )J 345 91 :M -.037(removal )A 381 91 :M .144 .014(of )J 393 91 :M .047 .005(one )J 411 91 :M -.344(edge )A 432 91 :M -.336(\(directed )A 468 91 :M .144 .014(or )J 480 91 :M -.053(bi-)A 59 103 :M -.05(directed\) from )A f2_10 sf -.105(M)A f1_10 sf -.048(, or reversal of one directed edge in )A f2_10 sf -.105(M)A f1_10 sf -.049(. If none of these )A 347 103 :M -.101(changes )A 382 103 :M .16 .016(improves )J 423 103 :M .218 .022(the )J 439 103 :M -.056(BIC )A 459 103 :M -.119(score )A 483 103 :M -.328(of)A 59 115 :M f2_10 sf .16(M)A f1_10 sf .269 .027(, the algorithm halts and outputs )J f2_10 sf .16(M)A f1_10 sf .279 .028(. Otherwise the change that most )J 347 115 :M .16 .016(improves )J 388 115 :M .218 .022(the )J 404 115 :M -.056(BIC )A 424 115 :M -.119(score )A 448 115 :M .694 .069(is )J 459 115 :M -.289(made )A 483 115 :M .222(to)A 59 127 :M f2_10 sf -.103(M)A f1_10 sf -.05( and the process is repeated.)A 59 143 :M (Even )S 83 143 :M .236 .024(at )J 94 143 :M -.097(large )A 117 143 :M .111 .011(sample )J 149 143 :M .354 .035(sizes, )J 175 143 :M .753 .075(this )J 194 143 :M -.172(search )A 222 143 :M -.1(suffers )A 252 143 :M .047 .005(from )J 275 143 :M .218 .022(the )J 291 143 :M .325 .033(following )J 334 143 :M .376 .038(problem. )J 374 143 :M .419 .042(At )J 388 143 :M -.204(each )A 409 143 :M .285 .028(stage, )J 436 143 :M -.097(there )A 460 143 :M .218 .022(may )J 482 143 :M -.439(be)A 59 155 :M .012 .001(many MAGs that receive the same BIC score, and the algorithm arbitrarily chooses one of them. While )J 476 155 :M (two)S 59 167 :M .202 .02(MAGs )J 90 167 :M .555 .056(M )J 103 167 :M -.313(and )A 120 167 :M .236 .024<4DD520>J 136 167 :M .218 .022(may )J 157 167 :M -.194(receive )A 188 167 :M .218 .022(the )J 204 167 :M (same )S 228 167 :M -.056(BIC )A 248 167 :M -.016(score, )A 275 167 :M .218 .022(the )J 291 167 :M .047 .005(one )J 309 167 :M -.344(edge )A 330 167 :M -.05(modification )A 384 167 :M .601 .06(to )J 396 167 :M .555 .056(M )J 409 167 :M .218 .022(may )J 430 167 :M -.194(receive )A 461 167 :M .056 .006(a )J 469 167 :M -.072(much)A 59 179 :M (higher )S 88 179 :M -.056(BIC )A 108 179 :M -.119(score )A 132 179 :M .202 .02(than )J 153 179 :M .218 .022(the )J 169 179 :M (same )S 193 179 :M .047 .005(one )J 212 179 :M -.344(edge )A 234 179 :M -.05(modification )A 289 179 :M .601 .06(to )J 302 179 :M .602 .06(M\325. )J 322 179 :M .359 .036(Thus )J 347 179 :M .328 .033(if )J 358 179 :M .218 .022(the )J 375 179 :M -.172(search )A 404 179 :M .41 .041(halts )J 428 179 :M -.039(when )A 454 179 :M .786 .079(it )J 465 179 :M -.131(cannot)A 59 191 :M .222 .022(improve the score, it may halt at M\325, which is a local rather that a global maximum.)J 59 214 :M f0_10 sf (V)S 67 214 :M (.)S 71 214 :M 21.5 2.15( )J 95 214 :M 2.306 .231(Greedy BIC PAG Search)J 59 232 :M f1_10 sf -.103(A greedy PAG search )A 148 232 :M .315 .032(solves )J 177 232 :M .281 .028(some )J 202 232 :M .144 .014(of )J 214 232 :M .218 .022(the )J 230 232 :M .16 .016(problems )J 271 232 :M -.159(associated )A 314 232 :M .517 .052(with )J 336 232 :M .056 .006(a )J 344 232 :M -.284(greedy )A 373 232 :M .132 .013(MAG )J 400 232 :M -.076(search. )A 431 232 :M 1.042 .104(First, )J 457 232 :M -.097(there )A 480 232 :M -.602(are)A 59 244 :M -.034(many fewer MAGs than PAGs. Second, MAGs that are score-equivalent )A 351 244 :M .5 .05( )J 355 244 :M .601 .06(in )J 367 244 :M .218 .022(the )J 383 244 :M -.031(sense )A 408 244 :M .361 .036(that )J 427 244 :M .202 .02(they )J 448 244 :M -.194(receive )A 479 244 :M -.108(the)A 59 256 :M -.026(same BIC )A 102 256 :M -.119(score )A 126 256 :M -.052(for )A 141 256 :M -.141(every )A 166 256 :M -.289(data )A 185 256 :M .303 .03(set )J 200 256 :M .676 .068(will )J 220 256 :M .388 .039(all )J 234 256 :M .051 .005(be )J 247 256 :M -.234(represented )A 294 256 :M .417 .042(by )J 308 256 :M .218 .022(the )J 324 256 :M (same )S 348 256 :M .716 .072(PAG, )J 375 256 :M -.313(and )A 392 256 :M .417 .042(no )J 406 256 :M .387 .039(two )J 425 256 :M .438 .044(PAGs )J 453 256 :M -.235(are )A 468 256 :M -.284(score-)A 59 268 :M -.099(equivalent. Hence )A 133 268 :M .218 .022(the )J 149 268 :M -.172(search )A 177 268 :M -.207(does )A 198 268 :M .555 .056(not )J 215 268 :M -.135(suffer )A 241 268 :M .047 .005(from )J 264 268 :M .218 .022(the )J 280 268 :M .104 .01(problem )J 317 268 :M .144 .014(of )J 329 268 :M .177 .018(having )J 360 268 :M .601 .06(to )J 372 268 :M -.044(choose )A 403 268 :M -.043(arbitrarily )A 446 268 :M .047 .005(from )J 469 268 :M -.072(many)A 59 280 :M -.161(score-equivalent )A 126 280 :M -.006(alternatives. )A 178 280 :M .5 .05( )J 182 280 :M (The )S 201 280 :M -.172(search )A 229 280 :M .694 .069(is )J 240 280 :M -.312(described )A 279 280 :M .043 .004(below )J 307 280 :M -.313(and )A 324 280 :M -.044(illustrated )A 367 280 :M .601 .06(in )J 380 280 :M .248 .025(Figure )J 411 280 :M .833 .083(3. )J 424 280 :M .328 .033(It )J 435 280 :M .694 .069(is )J 447 280 :M (basically )S 487 280 :M (a)S 59 292 :M -.054(latent variable versions of a search devised by C. Meek and described in Spirtes and Meek \(1995\).)A 59 320 :M -.154(procedure GBPS\(PAG; data\);)A 59 332 :M -.054(begin)A 59 344 :M -.043( MAG:=PAG-to-MAG\(PAG\);)A 59 356 :M -.161( current-score:=score\(MAG,data\);)A 59 368 :M -.137( max-score:=current-score;)A 59 380 :M -.08( while max-score <= current-score do)A 59 392 :M .301 .03( begin)J 59 404 :M -.14( new-PAG:=add-best-edge-to-PAG\(PAG\);)A 59 416 :M -.033( MAG:=PAG-to-MAG\(new-PAG\);)A 59 428 :M -.122( current-score:=score\(MAG,data\);)A 59 440 :M -.009( if current-score > max-score then)A 59 452 :M .371 .037( begin)J 59 464 :M -.052( max-score:=current-score;)A 59 476 :M .234 .023( PAG:=new-PAG;)J 59 488 :M .167 .017( end;)J 59 500 :M -.043( end;)A 59 512 :M -.137( current-score:=max-score;)A 59 524 :M -.08( while max-score <= current-score do)A 59 536 :M .301 .03( begin)J 59 548 :M -.095( new-PAG:=remove-worst-edge-in-PAG\(PAG\);)A 59 560 :M -.033( MAG:=PAG-to-MAG\(new-PAG\);)A 59 572 :M -.122( current-score:=score\(MAG,data\);)A 59 584 :M -.009( if current-score > max-score then)A 59 596 :M .371 .037( begin)J 59 608 :M -.052( max-score:=current-score;)A 59 620 :M .234 .023( PAG:=new-PAG;)J 59 632 :M .167 .017( end;)J 59 644 :M -.043( end;)A 84 644 :M .46 .046( )J 59 656 :M -.023( return\(PAG\);)A 59 668 :M -.406(end;)A endp %%Page: 7 7 %%BeginPageSetup initializepage (peter; page: 7 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC 59 51 :M f1_10 sf (The )S 78 51 :M -.172(search )A 106 51 :M .249 .025(starts )J 131 51 :M .517 .052(with )J 153 51 :M .281 .028(some )J 178 51 :M .688 .069(initial )J 206 51 :M .716 .072(PAG. )J 234 51 :M .517 .052(This )J 257 51 :M -.143(could )A 283 51 :M -.039(come )A 309 51 :M .047 .005(from )J 333 51 :M -.17(background )A 383 51 :M -.087(knowledge, )A 433 51 :M -.069(another )A 467 51 :M -.306(search)A 59 63 :M .086 .009(procedure such as FCI, or could simply be a PAG with )J 283 63 :M .417 .042(no )J 297 63 :M -.128(edges. )A 325 63 :M (The )S 344 63 :M .387 .039(PAG )J 368 63 :M .694 .069(is )J 379 63 :M .202 .02(then )J 400 63 :M -.174(turned )A 428 63 :M .674 .067(into )J 448 63 :M .056 .006(a )J 456 63 :M .132 .013(MAG )J 483 63 :M .222(in)A 59 75 :M .02 .002(order to assign a score to it. The search then looks for the single best edge to add to )J 396 75 :M .218 .022(the )J 412 75 :M .688 .069(initial )J 440 75 :M .716 .072(PAG. )J 467 75 :M .144 .014(In )J 479 75 :M -.108(the)A 59 87 :M -.053(example )A 96 87 :M .144 .014(of )J 108 87 :M .248 .025(Figure )J 138 87 :M .454 .045(3 )J 147 87 :M -.097(there )A 170 87 :M -.235(are )A 185 87 :M -.039(four )A 205 87 :M .385 .038(single )J 233 87 :M -.344(edge )A 254 87 :M .387 .039(PAG )J 279 87 :M .144 .014(extensions )J 326 87 :M .144 .014(of )J 339 87 :M .218 .022(the )J 356 87 :M .688 .069(initial )J 385 87 :M .716 .072(PAG. )J 413 87 :M -.121(Each )A 437 87 :M .144 .014(of )J 450 87 :M (these )S 475 87 :M -.218(four)A 59 99 :M .19 .019(extensions is turned into a MAG in )J 205 99 :M -.319(order )A 228 99 :M .601 .06(to )J 240 99 :M -.119(score )A 264 99 :M 1.11 .111(it. )J 277 99 :M (The )S 296 99 :M .132 .013(MAG )J 323 99 :M .517 .052(with )J 345 99 :M .218 .022(the )J 361 99 :M .281 .028(best )J 381 99 :M -.119(score )A 405 99 :M .694 .069(is )J 416 99 :M .138 .014(chosen, )J 450 99 :M -.313(and )A 467 99 :M -.309(turned)A 59 111 :M -.004(back into its corresponding PAG. These steps are then repeated until the )A 351 111 :M -.119(score )A 375 111 :M -.026(cannot )A 405 111 :M .051 .005(be )J 418 111 :M -.036(improved. )A 462 111 :M .419 .042(At )J 476 111 :M .185(this)A 59 123 :M -.026(stage the search then removes edges until the score can no longer be improved.)A 169 145 211 184 rC 169.5 145.5 105 40 rS 170 146 103 39 rC gS .723 .724 scale 235.263 223.63 :M f1_12 sf (X)S gR gS .723 .724 scale 244.95 226.391 :M f0_7 sf (1)S gR gS .723 .724 scale 249.102 223.63 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 253.254 223.63 :M f1_12 sf (o)S gR gS .723 .724 scale 258.789 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 261.557 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 264.325 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 267.093 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 276.78 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 279.548 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 282.316 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 285.084 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 294.771 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 297.539 223.63 :M f1_12 sf (o)S gR gS .723 .724 scale 303.074 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 307.226 223.63 :M f1_12 sf (X)S gR gS .723 .724 scale 315.529 226.391 :M f1_7 sf (2)S gR gS .723 .724 scale 319.681 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 322.449 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 355.662 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 358.43 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 361.198 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 365.35 223.63 :M f1_12 sf (X)S gR gS .723 .724 scale 373.653 226.391 :M f1_7 sf (3)S gR gS .723 .724 scale 235.263 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 238.031 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 242.183 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 244.95 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 247.718 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 250.486 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 253.254 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 256.022 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 260.173 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 262.941 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 265.709 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 268.477 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 278.164 247.097 :M f1_12 sf (I)S gR gS .723 .724 scale 282.316 247.097 :M f1_12 sf (n)S gR gS .723 .724 scale 287.851 247.097 :M f1_12 sf (i)S gR gS .723 .724 scale 290.619 247.097 :M f1_12 sf (t)S gR gS .723 .724 scale 293.387 247.097 :M f1_12 sf (i)S gR gS .723 .724 scale 296.155 247.097 :M f1_12 sf (a)S gR gS .723 .724 scale 301.69 247.097 :M f1_12 sf (l)S gR gS .723 .724 scale 304.458 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 307.226 247.097 :M f1_12 sf (P)S gR gS .723 .724 scale 314.145 247.097 :M f1_12 sf (A)S gR gS .723 .724 scale 322.449 247.097 :M f1_12 sf (G)S gR gR gS 169 145 211 184 rC 186 160 -1 1 215 159 1 186 159 @a 274.5 145.5 104 40 rS 275 146 103 39 rC gS .723 .724 scale 380.573 223.63 :M f1_12 sf (X)S gR gS .723 .724 scale 390.26 226.391 :M f0_7 sf (1)S gR gS .723 .724 scale 393.028 223.63 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 397.179 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 401.331 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 404.099 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 406.867 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 409.635 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 412.402 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 415.17 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 419.322 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 422.09 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 424.857 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 427.625 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 430.393 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 433.161 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 437.313 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 440.08 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 442.848 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 445.616 223.63 :M f1_12 sf (X)S gR gS .723 .724 scale 455.303 226.391 :M f1_7 sf (2)S gR gS .723 .724 scale 458.071 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 462.223 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 464.991 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 467.758 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 470.526 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 473.294 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 476.062 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 480.214 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 482.981 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 485.749 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 488.517 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 491.285 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 494.053 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 498.204 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 500.972 223.63 :M f1_12 sf ( )S gR gS .723 .724 scale 503.74 223.63 :M f1_12 sf (X)S gR gS .723 .724 scale 512.043 226.391 :M f1_7 sf (3)S gR gS .723 .724 scale 380.573 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 383.34 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 386.108 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 390.26 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 393.028 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 395.796 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 398.563 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 401.331 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 404.099 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 408.251 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 411.018 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 413.786 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 416.554 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 419.322 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 422.09 247.097 :M f1_12 sf (I)S gR gS .723 .724 scale 426.241 247.097 :M f1_12 sf (n)S gR gS .723 .724 scale 433.161 247.097 :M f1_12 sf (i)S gR gS .723 .724 scale 435.929 247.097 :M f1_12 sf (t)S gR gS .723 .724 scale 438.697 247.097 :M f1_12 sf (i)S gR gS .723 .724 scale 441.464 247.097 :M f1_12 sf (a)S gR gS .723 .724 scale 447 247.097 :M f1_12 sf (l)S gR gS .723 .724 scale 449.768 247.097 :M f1_12 sf ( )S gR gS .723 .724 scale 452.536 247.097 :M f1_12 sf (M)S gR gS .723 .724 scale 462.223 247.097 :M f1_12 sf (A)S gR gS .723 .724 scale 470.526 247.097 :M f1_12 sf (G)S gR gR gS 169 145 211 184 rC 289 159 -1 1 314 158 1 289 158 @a np 311 155 :M 311 161 :L 317 158 :L 311 155 :L eofill -1 -1 312 162 1 1 311 155 @b -1 -1 312 162 1 1 317 158 @b 311 156 -1 1 318 158 1 311 155 @a 169.5 186.5 105 141 rS 170 187 103 140 rC gS .723 .724 scale 235.263 278.847 :M f1_12 sf (X)S gR gS .723 .724 scale 244.95 281.608 :M f0_7 sf (1)S gR gS .723 .724 scale 249.102 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 253.254 278.847 :M f1_12 sf (o)S gR gS .723 .724 scale 258.789 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 261.557 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 264.325 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 267.093 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 276.78 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 279.548 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 282.316 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 285.084 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 294.771 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 297.539 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 300.306 278.847 :M f1_12 sf (X)S gR gS .723 .724 scale 309.994 281.608 :M f1_7 sf (2)S gR gS .723 .724 scale 314.145 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 316.913 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 319.681 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 322.449 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 278.847 :M f1_12 sf (o)S gR gS .723 .724 scale 358.43 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 361.198 278.847 :M f1_12 sf (X)S gR gS .723 .724 scale 370.885 281.608 :M f1_7 sf (3)S gR gS .723 .724 scale 235.263 314.738 :M f1_12 sf (X)S gR gS .723 .724 scale 244.95 317.499 :M f0_7 sf (1)S gR gS .723 .724 scale 249.102 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 253.254 314.738 :M f1_12 sf (o)S gR gS .723 .724 scale 258.789 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 261.557 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 264.325 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 267.093 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 276.78 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 279.548 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 282.316 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 285.084 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 314.738 :M f1_12 sf (o)S gR gS .723 .724 scale 297.539 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 300.306 314.738 :M f1_12 sf (X)S gR gS .723 .724 scale 309.994 317.499 :M f1_7 sf (2)S gR gS .723 .724 scale 314.145 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 316.913 314.738 :M f1_12 sf (o)S gR gS .723 .724 scale 322.449 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 355.662 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 358.43 314.738 :M f1_12 sf (o)S gR gS .723 .724 scale 365.35 314.738 :M f1_12 sf (X)S gR gS .723 .724 scale 373.653 317.499 :M f1_7 sf (3)S gR gS .723 .724 scale 235.263 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 238.031 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 242.183 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 244.95 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 247.718 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 250.486 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 253.254 350.63 :M f1_12 sf (o)S gR gS .723 .724 scale 260.173 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 262.941 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 265.709 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 268.477 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 278.164 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 280.932 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 283.7 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 286.467 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 296.155 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 298.923 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 301.69 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 304.458 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 307.226 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 311.378 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 314.145 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 316.913 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 319.681 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 322.449 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 355.662 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 358.43 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 361.198 350.63 :M f1_12 sf ( )S gR gS .723 .724 scale 365.35 350.63 :M f1_12 sf (o)S gR gS .723 .724 scale 235.263 363.054 :M f1_12 sf (X)S gR gS .723 .724 scale 244.95 365.814 :M f0_7 sf (1)S gR gS .723 .724 scale 249.102 363.054 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 253.254 363.054 :M f1_12 sf (o)S gR gS .723 .724 scale 258.789 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 261.557 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 264.325 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 267.093 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 276.78 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 279.548 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 282.316 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 285.084 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 294.771 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 297.539 363.054 :M f1_12 sf (o)S gR gS .723 .724 scale 303.074 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 307.226 363.054 :M f1_12 sf (X)S gR gS .723 .724 scale 315.529 365.814 :M f1_7 sf (2)S gR gS .723 .724 scale 319.681 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 322.449 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 355.662 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 358.43 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 361.198 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 365.35 363.054 :M f1_12 sf (X)S gR gS .723 .724 scale 373.653 365.814 :M f1_7 sf (3)S gR gS .723 .724 scale 235.263 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 238.031 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 242.183 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 244.95 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 247.718 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 250.486 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 253.254 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 256.022 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 260.173 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 262.941 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 265.709 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 268.477 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 278.164 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 280.932 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 283.7 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 286.467 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 296.155 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 298.923 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 301.69 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 304.458 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 307.226 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 311.378 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 314.145 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 316.913 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 319.681 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 322.449 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 355.662 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 358.43 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 361.198 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 365.35 398.945 :M f1_12 sf ( )S gR gS .723 .724 scale 368.118 398.945 :M f1_12 sf (o)S gR gS .723 .724 scale 235.263 411.369 :M f1_12 sf (X)S gR gS .723 .724 scale 244.95 414.13 :M f0_7 sf (1)S gR gS .723 .724 scale 249.102 411.369 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 253.254 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 256.022 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 258.789 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 261.557 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 264.325 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 267.093 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 271.245 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 274.012 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 276.78 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 279.548 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 282.316 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 285.084 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 289.235 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 292.003 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 294.771 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 297.539 411.369 :M f1_12 sf (o)S gR gS .723 .724 scale 303.074 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 307.226 411.369 :M f1_12 sf (X)S gR gS .723 .724 scale 315.529 414.13 :M f1_7 sf (2)S gR gS .723 .724 scale 319.681 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 322.449 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 325.217 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 329.368 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 332.136 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 334.904 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 337.672 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 340.44 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 343.207 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 347.359 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 350.127 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 352.895 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 355.662 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 358.43 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 361.198 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 365.35 411.369 :M f1_12 sf (X)S gR gS .723 .724 scale 373.653 414.13 :M f1_7 sf (3)S gR gS .723 .724 scale 235.263 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 238.031 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 242.183 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 244.95 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 247.718 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 250.486 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 253.254 434.836 :M f1_12 sf (O)S gR gS .723 .724 scale 261.557 434.836 :M f1_12 sf (n)S gR gS .723 .724 scale 267.093 434.836 :M f1_12 sf (e)S gR gS .723 .724 scale 272.628 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 275.396 434.836 :M f1_12 sf (e)S gR gS .723 .724 scale 280.932 434.836 :M f1_12 sf (d)S gR gS .723 .724 scale 286.467 434.836 :M f1_12 sf (g)S gR gS .723 .724 scale 292.003 434.836 :M f1_12 sf (e)S gR gS .723 .724 scale 297.539 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 300.306 434.836 :M f1_12 sf (e)S gR gS .723 .724 scale 305.842 434.836 :M f1_12 sf (x)S gR gS .723 .724 scale 311.378 434.836 :M f1_12 sf (t)S gR gS .723 .724 scale 314.145 434.836 :M f1_12 sf (e)S gR gS .723 .724 scale 319.681 434.836 :M f1_12 sf (n)S gR gS .723 .724 scale 325.217 434.836 :M f1_12 sf (s)S gR gS .723 .724 scale 330.752 434.836 :M f1_12 sf (i)S gR gS .723 .724 scale 333.52 434.836 :M f1_12 sf (o)S gR gS .723 .724 scale 339.056 434.836 :M f1_12 sf (n)S gR gS .723 .724 scale 345.975 434.836 :M f1_12 sf (s)S gR gR gS 169 145 211 184 rC 186 226 -1 1 212 225 1 186 225 @a 233 227 -1 1 260 226 1 233 226 @a 186 201 -1 1 208 200 1 186 200 @a np 205 197 :M 205 203 :L 211 200 :L 205 197 :L eofill -1 -1 206 204 1 1 205 197 @b -1 -1 206 204 1 1 211 200 @b 205 198 -1 1 212 200 1 205 197 @a 234 201 -1 1 255 200 1 234 200 @a np 235 203 :M 235 197 :L 230 200 :L 235 203 :L eofill -1 -1 236 204 1 1 235 197 @b -1 -1 231 201 1 1 235 197 @b 230 201 -1 1 236 203 1 230 200 @a -180 -90 70 23 221.5 252 @n -90 0 85 21 222 251 @n 187 262 -1 1 216 261 1 187 261 @a 191 297 -1 1 216 296 1 191 296 @a np 193 299 :M 193 293 :L 187 296 :L 193 299 :L eofill -1 -1 194 300 1 1 193 293 @b -1 -1 188 297 1 1 193 293 @b 187 297 -1 1 194 299 1 187 296 @a -1 -1 177 287 1 1 176 284 @b np 178 284 :M 173 284 :L 176 290 :L 178 284 :L eofill 173 285 -1 1 179 284 1 173 284 @a 173 285 -1 1 177 290 1 173 284 @a -1 -1 177 291 1 1 178 284 @b -180 -90 76 29 214.5 285 @n -90 0 105 29 215 285 @n 274.5 186.5 104 141 rS 275 187 103 140 rC gS .723 .724 scale 380.573 278.847 :M f1_12 sf (X)S gR gS .723 .724 scale 390.26 281.608 :M f0_7 sf (1)S gR gS .723 .724 scale 393.028 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 397.179 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 401.331 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 405.483 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 409.635 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 413.786 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 417.938 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 422.09 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 426.241 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 429.009 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 433.161 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 437.313 278.847 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 441.464 278.847 :M f1_12 sf (X)S gR gS .723 .724 scale 451.152 281.608 :M f1_7 sf (2)S gR gS .723 .724 scale 455.303 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 458.071 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 460.839 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 463.607 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 466.375 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 469.142 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 473.294 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 476.062 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 478.83 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 481.597 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 484.365 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 487.133 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 491.285 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 494.053 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 496.82 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 499.588 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 502.356 278.847 :M f1_12 sf ( )S gR gS .723 .724 scale 505.124 278.847 :M f1_12 sf (X)S gR gS .723 .724 scale 514.811 281.608 :M f1_7 sf (3)S gR gS .723 .724 scale 380.573 314.738 :M f1_12 sf (X)S gR gS .723 .724 scale 390.26 317.499 :M f0_7 sf (1)S gR gS .723 .724 scale 393.028 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 397.179 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 401.331 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 405.483 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 409.635 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 413.786 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 417.938 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 422.09 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 426.241 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 429.009 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 433.161 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 437.313 314.738 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 441.464 314.738 :M f1_12 sf (X)S gR gS .723 .724 scale 451.152 317.499 :M f1_7 sf (2)S gR gS .723 .724 scale 455.303 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 458.071 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 460.839 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 463.607 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 466.375 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 469.142 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 473.294 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 476.062 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 478.83 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 481.597 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 484.365 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 487.133 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 491.285 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 494.053 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 496.82 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 499.588 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 502.356 314.738 :M f1_12 sf ( )S gR gS .723 .724 scale 505.124 314.738 :M f1_12 sf (X)S gR gS .723 .724 scale 514.811 317.499 :M f1_7 sf (3)S gR gS .723 .724 scale 380.573 363.054 :M f1_12 sf (X)S gR gS .723 .724 scale 390.26 365.814 :M f0_7 sf (1)S gR gS .723 .724 scale 393.028 363.054 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 397.179 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 401.331 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 404.099 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 406.867 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 409.635 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 412.402 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 415.17 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 419.322 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 422.09 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 424.857 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 427.625 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 430.393 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 433.161 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 437.313 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 440.08 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 442.848 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 445.616 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 448.384 363.054 :M f1_12 sf (X)S gR gS .723 .724 scale 458.071 365.814 :M f1_7 sf (2)S gR gS .723 .724 scale 462.223 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 464.991 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 467.758 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 470.526 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 473.294 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 476.062 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 480.214 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 482.981 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 485.749 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 488.517 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 491.285 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 494.053 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 498.204 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 500.972 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 503.74 363.054 :M f1_12 sf ( )S gR gS .723 .724 scale 506.508 363.054 :M f1_12 sf (X)S gR gS .723 .724 scale 516.195 365.814 :M f1_7 sf (3)S gR gS .723 .724 scale 380.573 411.369 :M f1_12 sf (X)S gR gS .723 .724 scale 390.26 414.13 :M f0_7 sf (1)S gR gS .723 .724 scale 393.028 411.369 :M f0_12 sf 1 .1( )J gR gS .723 .724 scale 397.179 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 401.331 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 404.099 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 406.867 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 409.635 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 412.402 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 415.17 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 419.322 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 422.09 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 424.857 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 427.625 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 430.393 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 433.161 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 437.313 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 440.08 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 442.848 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 445.616 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 448.384 411.369 :M f1_12 sf (X)S gR gS .723 .724 scale 458.071 414.13 :M f1_7 sf (2)S gR gS .723 .724 scale 462.223 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 464.991 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 467.758 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 470.526 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 473.294 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 476.062 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 480.214 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 482.981 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 485.749 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 488.517 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 491.285 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 494.053 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 498.204 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 500.972 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 503.74 411.369 :M f1_12 sf ( )S gR gS .723 .724 scale 506.508 411.369 :M f1_12 sf (X)S gR gS .723 .724 scale 516.195 414.13 :M f1_7 sf (3)S gR gS .723 .724 scale 380.573 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 383.34 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 386.108 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 390.26 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 393.028 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 395.796 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 398.563 434.836 :M f1_12 sf (C)S gR gS .723 .724 scale 406.867 434.836 :M f1_12 sf (o)S gR gS .723 .724 scale 412.402 434.836 :M f1_12 sf (r)S gR gS .723 .724 scale 416.554 434.836 :M f1_12 sf (r)S gR gS .723 .724 scale 420.706 434.836 :M f1_12 sf (e)S gR gS .723 .724 scale 426.241 434.836 :M f1_12 sf (s)S gR gS .723 .724 scale 430.393 434.836 :M f1_12 sf (p)S gR gS .723 .724 scale 437.313 434.836 :M f1_12 sf (o)S gR gS .723 .724 scale 442.848 434.836 :M f1_12 sf (n)S gR gS .723 .724 scale 448.384 434.836 :M f1_12 sf (d)S gR gS .723 .724 scale 455.303 434.836 :M f1_12 sf (i)S gR gS .723 .724 scale 458.071 434.836 :M f1_12 sf (n)S gR gS .723 .724 scale 463.607 434.836 :M f1_12 sf (g)S gR gS .723 .724 scale 469.142 434.836 :M f1_12 sf ( )S gR gS .723 .724 scale 473.294 434.836 :M f1_12 sf (M)S gR gS .723 .724 scale 482.981 434.836 :M f1_12 sf (A)S gR gS .723 .724 scale 491.285 434.836 :M f1_12 sf (G)S gR gS .723 .724 scale 499.588 434.836 :M f1_12 sf (s)S gR gR gS 169 145 211 184 rC 291 201 -1 1 312 200 1 291 200 @a np 310 197 :M 310 203 :L 316 200 :L 310 197 :L eofill -1 -1 311 204 1 1 310 197 @b -1 -1 311 204 1 1 316 200 @b 310 198 -1 1 317 200 1 310 197 @a 339 201 -1 1 360 200 1 339 200 @a np 340 203 :M 340 197 :L 334 200 :L 340 203 :L eofill -1 -1 341 204 1 1 340 197 @b -1 -1 335 201 1 1 340 197 @b 334 201 -1 1 341 203 1 334 200 @a -180 -90 81 29 326 255 @n -90 0 85 21 327 251 @n 296 297 -1 1 320 296 1 296 296 @a np 298 299 :M 298 293 :L 292 296 :L 298 299 :L eofill -1 -1 299 300 1 1 298 293 @b -1 -1 293 297 1 1 298 293 @b 292 297 -1 1 299 299 1 292 296 @a -1 -1 281 287 1 1 280 284 @b np 283 284 :M 277 284 :L 280 290 :L 283 284 :L eofill 277 285 -1 1 284 284 1 277 284 @a 277 285 -1 1 281 290 1 277 284 @a -1 -1 281 291 1 1 283 284 @b -180 -90 77 29 319 285 @n -90 0 105 29 320 285 @n 290 226 -1 1 312 225 1 290 225 @a np 309 223 :M 309 228 :L 315 225 :L 309 223 :L eofill -1 -1 310 229 1 1 309 223 @b -1 -1 310 229 1 1 315 225 @b 309 224 -1 1 316 225 1 309 223 @a 335 226 -1 1 356 225 1 335 225 @a np 354 223 :M 354 228 :L 360 225 :L 354 223 :L eofill -1 -1 355 229 1 1 354 223 @b -1 -1 355 229 1 1 360 225 @b 354 224 -1 1 361 225 1 354 223 @a -1 -1 370 252 1 1 369 250 @b np 372 250 :M 366 250 :L 369 256 :L 372 250 :L eofill 366 251 -1 1 373 250 1 366 250 @a 366 251 -1 1 370 256 1 366 250 @a -1 -1 370 257 1 1 372 250 @b 291 262 -1 1 312 261 1 291 261 @a np 310 258 :M 310 264 :L 316 261 :L 310 258 :L eofill -1 -1 311 265 1 1 310 258 @b -1 -1 311 265 1 1 316 261 @b 310 259 -1 1 317 261 1 310 258 @a gR gS 0 0 552 730 rC 254 346 :M f0_10 sf 3.634 .363(Figure 3)J 59 364 :M f1_10 sf -.188(We )A 76 364 :M -.114(conjecture )A 120 364 :M .361 .036(that )J 139 364 :M .753 .075(this )J 158 364 :M -.172(search )A 186 364 :M .694 .069(is )J 197 364 :M .261 .026(asymptotically )J 260 364 :M -.094(correct, )A 293 364 :M .144 .014(as )J 305 364 :M .515 .052(long )J 327 364 :M .144 .014(as )J 339 364 :M .218 .022(the )J 355 364 :M .178 .018(distribution )J 405 364 :M .694 .069(is )J 417 364 :M .218 .022(the )J 434 364 :M (marginal )S 474 364 :M .144 .014(of )J 487 364 :M (a)S 59 376 :M .219 .022(distribution faithful to )J 152 376 :M .281 .028(some )J 177 376 :M -.337(directed )A 210 376 :M -.116(acyclic )A 241 376 :M .146 .015(graph. )J 270 376 :M .328 .033(It )J 280 376 :M .694 .069(is )J 291 376 :M .19 .019(worst )J 317 376 :M -.176(case )A 337 376 :M -.014(exponential )A 387 376 :M .601 .06(in )J 399 376 :M .218 .022(the )J 415 376 :M (number )S 449 376 :M .144 .014(of )J 461 376 :M -.156(vertices)A 59 388 :M -.03(because of the remove-worst-edge-in-PAG step. In addition, we do not know the complexity of )A 441 388 :M .218 .022(the )J 457 388 :M -.072(PAG-to-)A 59 400 :M -.033(MAG step, because we do not know how much back-tracking may be needed in )A 380 400 :M -.319(order )A 403 400 :M .601 .06(to )J 415 400 :M .281 .028(turn )J 435 400 :M .056 .006(a )J 443 400 :M .387 .039(PAG )J 467 400 :M .674 .067(into )J 487 400 :M (a)S 59 412 :M .02 .002(MAG. We do not currently know the number of variables that this kind of search )J 387 412 :M -.126(can )A 404 412 :M -.019(feasibly )A 439 412 :M .051 .005(be )J 452 412 :M -.33(performed)A 59 424 :M -.006(on. The current implementation is not practical for 30 variables, but could be greatly speeded up.)A 59 447 :M f0_10 sf (V)S 67 447 :M (I)S 71 447 :M (.)S 75 447 :M 17.5 1.75( )J 95 447 :M 5.131 .513(Simulation Study)J 59 465 :M f1_10 sf (As a very preliminary )S 150 465 :M .64 .064(simulation )J 197 465 :M .208 .021(study, )J 225 465 :M -.079(we )A 240 465 :M -.053(chose )A 266 465 :M .387 .039(two )J 285 465 :M -.026(graphs )A 315 465 :M f2_10 sf .159(G)A f1_6 sf 0 2 rm .066(1)A 0 -2 rm f1_10 sf .055 .006( )J 329 465 :M -.313(and )A 346 465 :M f2_10 sf .159(G)A f1_6 sf 0 2 rm .066(2)A 0 -2 rm f1_10 sf .055 .006( )J 360 465 :M .517 .052(with )J 382 465 :M .18 .018(latent )J 408 465 :M -.065(variables )A 447 465 :M .04 .004(\(Figure )J 480 465 :M .086(4\),)A 59 477 :M -.065(and for sample )A 121 477 :M .044 .004(sizes )J 144 477 :M .667 .067(2500, )J 171 477 :M .667 .067(1000, )J 198 477 :M .714 .071(500, )J 220 477 :M -.313(and )A 237 477 :M .385 .038(250 )J 256 477 :M -.262(generated )A 296 477 :M .454 .045(5 )J 305 477 :M -.208(pseudo-rendom )A 368 477 :M .169 .017(samples )J 404 477 :M .047 .005(from )J 427 477 :M .67 .067(them. )J 454 477 :M (The )S 473 477 :M -.355(error)A 59 489 :M -.089(variables were standard normal, and the linear coefficients )A 291 489 :M -.231(were )A 313 489 :M -.116(between )A 349 489 :M .769 .077(0.5 )J 366 489 :M -.313(and )A 383 489 :M 1.071 .107(1.5, )J 403 489 :M -.313(and )A 420 489 :M -.426(did )A 435 489 :M .555 .056(not )J 452 489 :M -.067(vary )A 473 489 :M .075(with)A 59 501 :M .111 .011(sample )J 92 501 :M (size )S 112 501 :M .144 .014(or )J 125 501 :M .398 .04(sample. )J 161 501 :M (The )S 181 501 :M .629 .063(input )J 207 501 :M .601 .06(to )J 221 501 :M .218 .022(the )J 239 501 :M .327 .033(algorithm )J 284 501 :M .694 .069(is )J 297 501 :M .218 .022(the )J 315 501 :M -.131(data, )A 339 501 :M -.313(and )A 358 501 :M .218 .022(the )J 376 501 :M .59 .059(output )J 408 501 :M .694 .069(is )J 421 501 :M .056 .006(a )J 431 501 :M .716 .072(PAG. )J 460 501 :M -.385(Because)A 59 513 :M -.002(determining whether X is an ancestor of Y is important for predicting the )A 355 513 :M -.163(effects )A 384 513 :M .144 .014(of )J 396 513 :M .127 .013(interventions )J 452 513 :M .417 .042(on )J 466 513 :M .65 .065(X, )J 480 513 :M -.658(we)A 59 525 :M -.011(measure the performance of the algorithm by counting for )A 294 525 :M .216 .022(how )J 315 525 :M .202 .02(many )J 341 525 :M -.433(ordered )A 372 525 :M .044 .004(pairs )J 395 525 :M .144 .014(of )J 407 525 :M -.065(variables )A 446 525 :M .855 .085( )J 479 525 :M -.108(the)A 59 537 :M .59 .059(output )J 89 537 :M .387 .039(PAG )J 113 537 :M .623 .062(implies )J 147 537 :M .361 .036(that )J 166 537 :M .255 .026(X )J 177 537 :M .694 .069(is )J 188 537 :M .051 .005(an )J 201 537 :M -.101(ancestor )A 237 537 :M .144 .014(of )J 249 537 :M .255 .026(Y )J 260 537 :M -.089(\(#a )A 276 537 :M .601 .06(in )J 288 537 :M -.053(Table )A 314 537 :M .833 .083(1, )J 326 537 :M -.323(averaged )A 363 537 :M -.067(over )A 384 537 :M .218 .022(the )J 401 537 :M .454 .045(5 )J 411 537 :M .169 .017(samples )J 448 537 :M .236 .024(at )J 460 537 :M .056 .006(a )J 469 537 :M -.054(given)A 59 549 :M -.015(sample size\), and what percentage of the time the ancestor implication is correct )A 382 549 :M .601 .06(in )J 394 549 :M .218 .022(the )J 410 549 :M -.053(graph )A 436 549 :M .361 .036(that )J 455 549 :M -.357(generated)A 59 561 :M -.017(the data \(%ac, averaged over the 5 samples at a given sample size\). We construct similar )A 418 561 :M -.226(measured )A 458 561 :M -.052(for )A 473 561 :M -.109(non-)A 59 573 :M -.016(ancestor relations \(#na and %nac respectively\). In Table 1, size represents the sample size. In )A f2_10 sf (G)S f1_6 sf 0 2 rm (1)S 0 -2 rm f1_10 sf (, )S 449 573 :M .601 .06(in )J 461 573 :M .132 .013(20% )J 483 573 :M -.328(of)A 59 585 :M -.026(the ordered pairs of distinct measured variables , X is an ancestor of Y; )A 373 585 :M .601 .06(in )J 385 585 :M f2_10 sf .37(G)A f1_6 sf 0 2 rm .154(2)A 0 -2 rm f1_10 sf .233 .023(, )J 402 585 :M .601 .06(in )J 414 585 :M .132 .013(30% )J 436 585 :M .144 .014(of )J 448 585 :M .218 .022(the )J 464 585 :M -.589(ordered)A 59 597 :M .044 .004(pairs )J 82 597 :M .144 .014(of )J 94 597 :M .033 .003(distinct )J 127 597 :M -.226(measured )A 167 597 :M -.065(variables )A 206 597 :M 1.114 .111(, )J 242 597 :M .255 .026(X )J 253 597 :M .694 .069(is )J 264 597 :M .051 .005(an )J 277 597 :M -.101(ancestor )A 313 597 :M .144 .014(of )J 325 597 :M .65 .065(Y. )J 339 597 :M .144 .014(In )J 351 597 :M .218 .022(the )J 367 597 :M -.176(case )A 387 597 :M .144 .014(of )J 399 597 :M -.097(large )A 422 597 :M .111 .011(sample )J 454 597 :M .044 .004(sizes )J 478 597 :M -.719(and)A 59 609 :M -.011(sparse graphs, with perfectly normal data, and only a few latent variables, the algorithm performs )A 451 609 :M -.099(quite )A 474 609 :M -.071(well)A 59 621 :M -.148(\(see )A 78 621 :M -.053(Table )A 104 621 :M .517 .052(1\). )J 119 621 :M -.08(However, )A 161 621 :M -.079(we )A 176 621 :M -.099(expect )A 205 621 :M .218 .022(the )J 221 621 :M .192 .019(algorithm\325s )J 271 621 :M -.183(performance )A 323 621 :M .601 .06(to )J 335 621 :M .051 .005(be )J 348 621 :M .056 .006(a )J 356 621 :M .098 .01(function )J 393 621 :M .144 .014(of )J 405 621 :M .218 .022(the )J 421 621 :M -.344(edge )A 443 621 :M -.094(coefficients,)A 59 633 :M .216 .022(how )J 80 633 :M .202 .02(many )J 106 633 :M -.074(vertices )A 140 633 :M -.204(each )A 161 633 :M -.081(vertex )A 189 633 :M .601 .06(in )J 201 633 :M .218 .022(the )J 217 633 :M -.053(graph )A 243 633 :M .694 .069(is )J 254 633 :M -.226(adjacent )A 289 633 :M .94 .094(to, )J 304 633 :M .218 .022(the )J 320 633 :M .111 .011(sample )J 353 633 :M .304 .03(size, )J 376 633 :M .218 .022(the )J 393 633 :M (number )S 428 633 :M -.313(and )A 446 633 :M .16 .016(strength )J 483 633 :M -.328(of)A 59 645 :M .18 .018(latent )J 86 645 :M -.009(variables, )A 129 645 :M .218 .022(the )J 146 645 :M .315 .032(amount )J 181 645 :M .144 .014(of )J 194 645 :M (selection )S 234 645 :M .596 .06(bias, )J 258 645 :M -.313(and )A 276 645 :M -.06(deviations )A 321 645 :M .047 .005(from )J 345 645 :M .56 .056(normality. )J 392 645 :M .144 .014(In )J 405 645 :M -.319(order )A 429 645 :M .601 .06(to )J 442 645 :M -.101(evaluate )A 479 645 :M -.108(the)A 59 657 :M .192 .019(algorithm\325s )J 109 657 :M -.183(performance )A 161 657 :M .202 .02(much )J 187 657 :M (more )S 211 657 :M -.029(extensive )A 252 657 :M .64 .064(simulation )J 299 657 :M .484 .048(tests )J 321 657 :M -.235(are )A 336 657 :M -.331(needed, )A 368 657 :M .144 .014(as )J 380 657 :M .204 .02(well )J 401 657 :M .144 .014(as )J 413 657 :M .083 .008(applications )J 465 657 :M .601 .06(to )J 477 657 :M -.328(real)A 59 669 :M -.289(data.)A endp %%Page: 8 8 %%BeginPageSetup initializepage (peter; page: 8 of 8)setjob %%EndPageSetup gS 0 0 552 730 rC .75 lw 126 41 297 125 rC 126.5 41.5 147 59 rS 128 43 145 57 rC gS .788 .791 scale 161.209 63.203 :M f1_12 sf (X)S gR gS .788 .791 scale 171.364 65.731 :M f1_7 sf (1)S gR gS .788 .791 scale 175.172 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 177.711 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 180.25 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 184.058 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 186.597 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 190.405 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 192.943 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 195.482 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 199.29 63.203 :M f1_12 sf (T)S gR gS .788 .791 scale 205.637 65.731 :M f1_7 sf (1)S gR gS .788 .791 scale 209.445 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 215.792 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 218.331 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 222.139 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 224.677 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 227.216 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 231.024 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 233.563 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 63.203 :M f1_12 sf (X)S gR gS .788 .791 scale 246.257 65.731 :M f1_7 sf (2)S gR gS .788 .791 scale 250.065 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 252.603 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 256.412 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 258.95 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 261.489 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 265.297 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 267.836 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 270.375 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 274.183 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 276.721 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 279.26 63.203 :M f1_12 sf (T)S gR gS .788 .791 scale 286.876 65.731 :M f1_7 sf (2)S gR gS .788 .791 scale 290.684 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 293.223 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 297.031 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 299.57 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 303.378 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 305.917 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 308.455 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 312.264 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 314.802 63.203 :M f1_12 sf (X)S gR gS .788 .791 scale 323.688 65.731 :M f1_7 sf (3)S gR gS .788 .791 scale 161.209 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 165.017 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 167.556 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 171.364 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 173.903 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 176.442 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 180.25 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 182.788 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 185.327 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 189.135 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 191.674 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 194.213 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 198.021 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 200.56 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 204.368 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 206.906 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 209.445 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 215.792 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 218.331 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 222.139 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 224.677 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 227.216 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 231.024 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 233.563 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 239.91 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 242.449 98.596 :M f1_12 sf (X)S gR gS .788 .791 scale 251.334 101.124 :M f1_7 sf (4)S gR gS .788 .791 scale 256.412 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 258.95 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 261.489 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 265.297 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 267.836 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 270.375 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 274.183 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 276.721 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 279.26 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 283.068 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 285.607 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 289.415 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 291.954 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 294.492 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 298.301 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 300.839 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 303.378 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 307.186 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 309.725 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 312.264 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 316.072 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 318.61 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 322.418 98.596 :M f1_12 sf (X)S gR gS .788 .791 scale 331.304 101.124 :M f1_7 sf (5)S gR gS .788 .791 scale 161.209 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 165.017 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 167.556 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 171.364 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 173.903 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 176.442 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 180.25 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 182.788 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 185.327 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 189.135 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 191.674 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 194.213 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 198.021 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 200.56 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 204.368 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 206.906 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 209.445 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 215.792 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 218.331 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 222.139 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 224.677 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 227.216 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 231.024 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 233.563 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 122.613 :M f2_12 sf (G)S gR gS .788 .791 scale 246.257 125.141 :M f1_7 sf (1)S gR gR gS 126 41 297 125 rC 143 47.75 -.75 .75 152.75 47 .75 143 47 @a np 145 48 :M 145 45 :L 139 47 :L 145 48 :L .75 lw eofill -.75 -.75 145.75 48.75 .75 .75 145 45 @b -.75 -.75 139.75 47.75 .75 .75 145 45 @b 139 47.75 -.75 .75 145.75 48 .75 139 47 @a 206 47.75 -.75 .75 214.75 47 .75 206 47 @a np 207 48 :M 207 45 :L 201 47 :L 207 48 :L eofill -.75 -.75 207.75 48.75 .75 .75 207 45 @b -.75 -.75 201.75 47.75 .75 .75 207 45 @b 201 47.75 -.75 .75 207.75 48 .75 201 47 @a 168 47.75 -.75 .75 178.75 47 .75 168 47 @a np 176 45 :M 176 48 :L 183 47 :L 176 45 :L eofill -.75 -.75 176.75 48.75 .75 .75 176 45 @b -.75 -.75 176.75 48.75 .75 .75 183 47 @b 176 45.75 -.75 .75 183.75 47 .75 176 45 @a 231 47.75 -.75 .75 241.75 47 .75 231 47 @a np 239 45 :M 239 48 :L 246 47 :L 239 45 :L eofill -.75 -.75 239.75 48.75 .75 .75 239 45 @b -.75 -.75 239.75 48.75 .75 .75 246 47 @b 239 45.75 -.75 .75 246.75 47 .75 239 45 @a -.75 -.75 193.75 63.75 .75 .75 193 54 @b np 195 62 :M 191 62 :L 193 68 :L 195 62 :L eofill 191 62.75 -.75 .75 195.75 62 .75 191 62 @a 191 62.75 -.75 .75 193.75 68 .75 191 62 @a -.75 -.75 193.75 68.75 .75 .75 195 62 @b -.75 -.75 255.75 64.75 .75 .75 255 53 @b np 257 62 :M 254 62 :L 255 69 :L 257 62 :L eofill 254 62.75 -.75 .75 257.75 62 .75 254 62 @a 254 62.75 -.75 .75 255.75 69 .75 254 62 @a -.75 -.75 255.75 69.75 .75 .75 257 62 @b 206 74.75 -.75 .75 243.75 74 .75 206 74 @a np 241 73 :M 241 76 :L 247 74 :L 241 73 :L eofill -.75 -.75 241.75 76.75 .75 .75 241 73 @b -.75 -.75 241.75 76.75 .75 .75 247 74 @b 241 73.75 -.75 .75 247.75 74 .75 241 73 @a 274.5 41.5 147 59 rS 276 43 145 57 rC gS .788 .791 scale 350.344 63.203 :M f1_12 sf (X)S gR gS .788 .791 scale 359.23 65.731 :M f1_7 sf (1)S gR gS .788 .791 scale 363.038 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 365.577 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 369.385 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 371.924 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 374.462 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 378.271 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 380.809 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 383.348 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 387.156 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 389.695 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 392.234 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 396.042 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 398.58 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 402.388 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 404.927 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 407.466 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 411.274 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 413.813 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 416.351 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 420.16 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 422.698 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 425.237 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 429.045 63.203 :M f1_12 sf (X)S gR gS .788 .791 scale 437.931 65.731 :M f1_7 sf (2)S gR gS .788 .791 scale 441.739 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 444.277 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 448.086 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 450.624 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 454.432 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 456.971 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 459.51 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 463.318 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 465.857 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 468.395 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 472.203 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 474.742 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 477.281 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 481.089 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 483.628 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 487.436 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 489.975 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 492.513 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 496.321 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 498.86 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 501.399 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 505.207 63.203 :M f1_12 sf ( )S gR gS .788 .791 scale 507.746 63.203 :M f1_12 sf (X)S gR gS .788 .791 scale 516.631 65.731 :M f1_7 sf (3)S gR gS .788 .791 scale 350.344 98.596 :M f1_12 sf (X)S gR gS .788 .791 scale 359.23 101.124 :M f1_7 sf (6)S gR gS .788 .791 scale 363.038 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 365.577 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 369.385 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 371.924 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 374.462 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 378.271 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 380.809 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 383.348 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 387.156 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 389.695 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 392.234 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 396.042 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 398.58 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 402.388 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 404.927 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 407.466 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 411.274 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 413.813 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 416.351 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 420.16 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 422.698 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 425.237 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 429.045 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 431.584 98.596 :M f1_12 sf (X)S gR gS .788 .791 scale 440.469 101.124 :M f1_7 sf (5)S gR gS .788 .791 scale 444.277 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 448.086 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 450.624 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 454.432 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 456.971 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 459.51 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 463.318 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 465.857 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 468.395 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 472.203 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 474.742 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 477.281 98.596 :M f1_12 sf (T)S gR gS .788 .791 scale 484.897 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 487.436 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 491.244 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 493.783 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 496.321 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 500.129 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 502.668 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 505.207 98.596 :M f1_12 sf ( )S gR gS .788 .791 scale 509.015 98.596 :M f1_12 sf (X)S gR gS .788 .791 scale 517.901 101.124 :M f1_7 sf (4)S gR gS .788 .791 scale 350.344 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 352.883 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 355.422 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 359.23 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 361.769 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 364.307 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 368.116 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 370.654 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 373.193 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 377.001 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 379.54 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 383.348 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 385.887 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 388.425 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 392.234 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 394.772 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 397.311 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 401.119 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 403.658 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 406.197 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 410.005 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 412.543 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 416.351 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 418.89 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 421.429 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 425.237 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 427.776 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 430.314 122.613 :M f1_12 sf ( )S gR gS .788 .791 scale 434.123 122.613 :M f2_12 sf (G)S gR gS .788 .791 scale 443.008 125.141 :M f1_7 sf (2)S gR gR .75 lw gS 126 41 297 125 rC 126.5 100.5 147 64 rS 128 102 145 62 rC gS .788 .791 scale 161.209 137.782 :M f1_12 sf (X)S gR gS .788 .791 scale 171.364 140.31 :M f1_7 sf (1)S gR gS .788 .791 scale 175.172 137.782 :M f1_12 sf (o)S gR gS .788 .791 scale 180.25 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 184.058 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 186.597 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 190.405 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 192.943 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 195.482 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 199.29 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 201.829 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 204.368 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 208.176 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 210.714 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 217.061 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 219.6 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 223.408 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 225.947 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 228.486 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 232.294 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 234.832 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 241.179 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 243.718 137.782 :M f1_12 sf (X)S gR gS .788 .791 scale 252.603 140.31 :M f1_7 sf (2)S gR gS .788 .791 scale 256.412 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 260.22 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 262.758 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 265.297 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 269.105 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 271.644 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 274.183 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 277.991 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 280.529 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 284.338 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 286.876 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 289.415 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 293.223 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 295.762 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 298.301 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 302.109 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 304.647 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 307.186 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 310.994 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 313.533 137.782 :M f1_12 sf (o)S gR gS .788 .791 scale 319.88 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 322.418 137.782 :M f1_12 sf (X)S gR gS .788 .791 scale 331.304 140.31 :M f1_7 sf (3)S gR gS .788 .791 scale 161.209 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 165.017 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 167.556 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 171.364 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 173.903 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 176.442 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 180.25 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 182.788 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 185.327 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 189.135 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 191.674 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 194.213 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 198.021 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 200.56 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 204.368 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 206.906 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 209.445 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 215.792 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 218.331 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 222.139 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 224.677 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 227.216 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 231.024 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 233.563 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 239.91 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 242.449 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 246.257 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 248.795 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 251.334 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 255.142 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 257.681 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 260.22 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 264.028 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 266.566 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 270.375 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 272.913 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 275.452 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 279.26 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 281.799 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 284.338 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 288.146 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 290.684 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 293.223 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 297.031 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 299.57 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 303.378 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 305.917 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 308.455 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 312.264 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 314.802 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 317.341 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 321.149 149.158 :M f1_12 sf ( )S gR gS .788 .791 scale 323.688 149.158 :M f1_12 sf (o)S gR gS .788 .791 scale 161.209 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 165.017 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 167.556 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 171.364 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 173.903 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 176.442 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 180.25 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 182.788 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 185.327 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 189.135 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 191.674 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 194.213 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 198.021 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 200.56 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 204.368 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 206.906 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 209.445 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 215.792 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 218.331 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 222.139 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 224.677 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 227.216 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 231.024 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 233.563 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 239.91 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 242.449 173.175 :M f1_12 sf (X)S gR gS .788 .791 scale 251.334 176.967 :M f1_7 sf (4)S gR gS .788 .791 scale 256.412 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 258.95 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 261.489 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 265.297 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 267.836 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 270.375 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 274.183 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 276.721 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 279.26 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 283.068 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 285.607 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 289.415 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 291.954 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 294.492 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 298.301 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 300.839 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 303.378 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 307.186 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 309.725 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 312.264 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 316.072 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 318.61 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 322.418 173.175 :M f1_12 sf (X)S gR gS .788 .791 scale 331.304 176.967 :M f1_7 sf (5)S gR gS .788 .791 scale 161.209 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 165.017 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 167.556 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 171.364 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 173.903 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 176.442 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 180.25 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 182.788 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 185.327 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 189.135 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 191.674 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 194.213 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 198.021 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 200.56 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 204.368 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 206.906 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 209.445 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 213.253 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 215.792 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 218.331 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 222.139 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 224.677 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 227.216 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 231.024 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 233.563 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 237.371 197.192 :M f1_12 sf (P)S gR gS .788 .791 scale 243.718 197.192 :M f1_12 sf (A)S gR gS .788 .791 scale 251.334 197.192 :M f1_12 sf (G)S gR gS .788 .791 scale 260.22 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 264.028 197.192 :M f1_12 sf (f)S gR gS .788 .791 scale 267.836 197.192 :M f1_12 sf (o)S gR gS .788 .791 scale 274.183 197.192 :M f1_12 sf (r)S gR gS .788 .791 scale 277.991 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 280.529 197.192 :M f2_12 sf (G)S gR gS .788 .791 scale 289.415 200.984 :M f1_7 sf (1)S gR gR gS 126 41 297 125 rC -.75 -.75 193.75 122.75 .75 .75 193 113 @b np 195 121 :M 191 121 :L 193 127 :L 195 121 :L eofill 191 121.75 -.75 .75 195.75 121 .75 191 121 @a 191 121.75 -.75 .75 193.75 127 .75 191 121 @a -.75 -.75 193.75 127.75 .75 .75 195 121 @b -.75 -.75 257.75 126.75 .75 .75 257 119 @b np 258 125 :M 255 125 :L 257 131 :L 258 125 :L eofill 255 125.75 -.75 .75 258.75 125 .75 255 125 @a 255 125.75 -.75 .75 257.75 131 .75 255 125 @a -.75 -.75 257.75 131.75 .75 .75 258 125 @b 206 134.75 -.75 .75 243.75 134 .75 206 134 @a np 241 132 :M 241 135 :L 247 134 :L 241 132 :L eofill -.75 -.75 241.75 135.75 .75 .75 241 132 @b -.75 -.75 241.75 135.75 .75 .75 247 134 @b 241 132.75 -.75 .75 247.75 134 .75 241 132 @a 143 107.75 -.75 .75 175.75 107 .75 143 107 @a np 173 105 :M 173 108 :L 180 107 :L 173 105 :L eofill -.75 -.75 173.75 108.75 .75 .75 173 105 @b -.75 -.75 173.75 108.75 .75 .75 180 107 @b 173 105.75 -.75 .75 180.75 107 .75 173 105 @a 213 107.75 -.75 .75 247.75 107 .75 213 107 @a np 214 108 :M 214 105 :L 208 107 :L 214 108 :L eofill -.75 -.75 214.75 108.75 .75 .75 214 105 @b -.75 -.75 208.75 107.75 .75 .75 214 105 @b 208 107.75 -.75 .75 214.75 108 .75 208 107 @a 288 47.75 -.75 .75 331.75 47 .75 288 47 @a np 329 46 :M 329 49 :L 336 47 :L 329 46 :L eofill -.75 -.75 329.75 49.75 .75 .75 329 46 @b -.75 -.75 329.75 49.75 .75 .75 336 47 @b 329 46.75 -.75 .75 336.75 47 .75 329 46 @a 354 48.75 -.75 .75 399.75 48 .75 354 48 @a np 356 50 :M 356 47 :L 350 48 :L 356 50 :L eofill -.75 -.75 356.75 50.75 .75 .75 356 47 @b -.75 -.75 350.75 48.75 .75 .75 356 47 @b 350 48.75 -.75 .75 356.75 50 .75 350 48 @a 274.5 100.5 147 64 rS 276 102 145 62 rC gS .788 .791 scale 350.344 137.782 :M f1_12 sf (X)S gR gS .788 .791 scale 359.23 140.31 :M f1_7 sf (1)S gR gS .788 .791 scale 363.038 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 365.577 137.782 :M f1_12 sf (o)S gR gS .788 .791 scale 371.924 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 374.462 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 378.271 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 380.809 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 383.348 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 387.156 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 389.695 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 392.234 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 396.042 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 398.58 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 402.388 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 404.927 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 407.466 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 411.274 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 413.813 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 416.351 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 420.16 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 422.698 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 425.237 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 429.045 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 431.584 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 435.392 137.782 :M f1_12 sf (X)S gR gS .788 .791 scale 444.277 140.31 :M f1_7 sf (2)S gR gS .788 .791 scale 448.086 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 450.624 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 454.432 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 456.971 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 459.51 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 463.318 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 465.857 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 468.395 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 472.203 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 474.742 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 477.281 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 481.089 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 483.628 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 487.436 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 489.975 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 492.513 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 496.321 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 498.86 137.782 :M f1_12 sf (o)S gR gS .788 .791 scale 505.207 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 507.746 137.782 :M f1_12 sf ( )S gR gS .788 .791 scale 510.284 137.782 :M f1_12 sf (X)S gR gS .788 .791 scale 520.439 140.31 :M f1_7 sf (3)S gR gS .788 .791 scale 350.344 173.175 :M f1_12 sf (X)S gR gS .788 .791 scale 359.23 176.967 :M f1_7 sf (6)S gR gS .788 .791 scale 363.038 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 365.577 173.175 :M f1_12 sf (o)S gR gS .788 .791 scale 371.924 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 374.462 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 378.271 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 380.809 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 383.348 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 387.156 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 389.695 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 392.234 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 396.042 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 398.58 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 402.388 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 404.927 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 407.466 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 411.274 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 413.813 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 416.351 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 420.16 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 422.698 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 425.237 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 429.045 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 431.584 173.175 :M f1_12 sf (X)S gR gS .788 .791 scale 440.469 176.967 :M f1_7 sf (5)S gR gS .788 .791 scale 444.277 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 448.086 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 450.624 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 454.432 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 456.971 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 459.51 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 463.318 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 465.857 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 468.395 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 472.203 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 474.742 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 477.281 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 481.089 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 483.628 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 487.436 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 489.975 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 492.513 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 496.321 173.175 :M f1_12 sf ( )S gR gS .788 .791 scale 498.86 173.175 :M f1_12 sf (X)S gR gS .788 .791 scale 507.746 176.967 :M f1_7 sf (4)S gR gS .788 .791 scale 350.344 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 352.883 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 355.422 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 359.23 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 361.769 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 364.307 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 368.116 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 370.654 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 373.193 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 377.001 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 379.54 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 383.348 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 385.887 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 388.425 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 392.234 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 394.772 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 397.311 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 401.119 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 403.658 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 406.197 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 410.005 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 412.543 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 416.351 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 418.89 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 421.429 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 425.237 197.192 :M f1_12 sf (P)S gR gS .788 .791 scale 431.584 197.192 :M f1_12 sf (A)S gR gS .788 .791 scale 439.2 197.192 :M f1_12 sf (G)S gR gS .788 .791 scale 449.355 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 451.894 197.192 :M f1_12 sf (f)S gR gS .788 .791 scale 455.702 197.192 :M f1_12 sf (o)S gR gS .788 .791 scale 462.049 197.192 :M f1_12 sf (r)S gR gS .788 .791 scale 465.857 197.192 :M f1_12 sf ( )S gR gS .788 .791 scale 468.395 197.192 :M f2_12 sf (G)S gR gS .788 .791 scale 477.281 200.984 :M f1_7 sf (2)S gR gR gS 126 41 297 125 rC 294 107.75 -.75 .75 331.75 107 .75 294 107 @a np 329 105 :M 329 108 :L 336 107 :L 329 105 :L eofill -.75 -.75 329.75 108.75 .75 .75 329 105 @b -.75 -.75 329.75 108.75 .75 .75 336 107 @b 329 105.75 -.75 .75 336.75 107 .75 329 105 @a 360 106.75 -.75 .75 393.75 106 .75 360 106 @a np 362 107 :M 362 104 :L 355 106 :L 362 107 :L eofill -.75 -.75 362.75 107.75 .75 .75 362 104 @b -.75 -.75 355.75 106.75 .75 .75 362 104 @b 355 106.75 -.75 .75 362.75 107 .75 355 106 @a 358 134.75 -.75 .75 386.75 134 .75 358 134 @a np 384 133 :M 384 136 :L 391 134 :L 384 133 :L eofill -.75 -.75 384.75 136.75 .75 .75 384 133 @b -.75 -.75 384.75 136.75 .75 .75 391 134 @b 384 133.75 -.75 .75 391.75 134 .75 384 133 @a np 360 136 :M 360 133 :L 354 134 :L 360 136 :L eofill -.75 -.75 360.75 136.75 .75 .75 360 133 @b -.75 -.75 354.75 134.75 .75 .75 360 133 @b 354 134.75 -.75 .75 360.75 136 .75 354 134 @a 347 55.75 -.75 .75 394.75 69 .75 347 55 @a np 393 67 :M 392 70 :L 399 70 :L 393 67 :L eofill -.75 -.75 392.75 70.75 .75 .75 393 67 @b 392 70.75 -.75 .75 399.75 70 .75 392 70 @a 393 67.75 -.75 .75 399.75 70 .75 393 67 @a -.75 -.75 404.75 64.75 .75 .75 404 53 @b np 406 62 :M 403 62 :L 404 69 :L 406 62 :L eofill 403 62.75 -.75 .75 406.75 62 .75 403 62 @a 403 62.75 -.75 .75 404.75 69 .75 403 62 @a -.75 -.75 404.75 69.75 .75 .75 406 62 @b 291 76.75 -.75 .75 332.75 76 .75 291 76 @a np 331 74 :M 331 77 :L 337 76 :L 331 74 :L eofill -.75 -.75 331.75 77.75 .75 .75 331 74 @b -.75 -.75 331.75 77.75 .75 .75 337 76 @b 331 74.75 -.75 .75 337.75 76 .75 331 74 @a 357 76.75 -.75 .75 371.75 76 .75 357 76 @a np 358 77 :M 358 74 :L 352 76 :L 358 77 :L eofill -.75 -.75 358.75 77.75 .75 .75 358 74 @b -.75 -.75 352.75 76.75 .75 .75 358 74 @b 352 76.75 -.75 .75 358.75 77 .75 352 76 @a 386 76.75 -.75 .75 394.75 76 .75 386 76 @a np 392 74 :M 392 77 :L 399 76 :L 392 74 :L eofill -.75 -.75 392.75 77.75 .75 .75 392 74 @b -.75 -.75 392.75 77.75 .75 .75 399 76 @b 392 74.75 -.75 .75 399.75 76 .75 392 74 @a -.75 -.75 395.75 123.75 .75 .75 395 116 @b np 397 122 :M 394 122 :L 395 128 :L 397 122 :L eofill 394 122.75 -.75 .75 397.75 122 .75 394 122 @a 394 122.75 -.75 .75 395.75 128 .75 394 122 @a -.75 -.75 395.75 128.75 .75 .75 397 122 @b 346 113.75 -.75 .75 384.75 128 .75 346 113 @a np 384 126 :M 383 129 :L 389 130 :L 384 126 :L eofill -.75 -.75 383.75 129.75 .75 .75 384 126 @b 383 129.75 -.75 .75 389.75 130 .75 383 129 @a 384 126.75 -.75 .75 389.75 130 .75 384 126 @a 281 124 10 14 rC gS .788 .791 scale 356.691 165.591 :M f1_12 sf (o)S gR gR gS 281 111 10 13 rC gS .788 .791 scale 356.691 149.158 :M f1_12 sf (o)S gR gR gS 394 109 6 11 rC gS .788 .791 scale 500.129 146.63 :M f1_12 sf (o)S gR gR gS 126 41 297 125 rC -1 -1 284 128 1 1 283 117 @b 291 134.75 -.75 .75 332.75 134 .75 291 134 @a np 330 133 :M 330 136 :L 336 134 :L 330 133 :L eofill -.75 -.75 330.75 136.75 .75 .75 330 133 @b -.75 -.75 330.75 136.75 .75 .75 336 134 @b 330 133.75 -.75 .75 336.75 134 .75 330 133 @a -.75 -.75 281.75 67.75 .75 .75 281 57 @b np 280 58 :M 283 58 :L 281 52 :L 280 58 :L eofill 280 58.75 -.75 .75 283.75 58 .75 280 58 @a 281 52.75 -.75 .75 283.75 58 .75 281 52 @a -.75 -.75 280.75 58.75 .75 .75 281 52 @b 15 12 224 48.5 @f 15 13 160 48 @f 15 13 379 76 @f gR gS 0 0 552 730 rC 254 183 :M f0_10 sf 3.634 .363(Figure 4)J 94 199 200 24 rC 189 221 :M f2_10 sf -.155(G)A f1_6 sf 0 2 rm (1)S 0 -2 rm gR gS 295 199 200 24 rC 391 221 :M f2_10 sf -.155(G)A f1_6 sf 0 2 rm (2)S 0 -2 rm gR gS 0 0 552 730 rC 53 199 1 1 rF 53 199 1 1 rF 54 199 39 1 rF 93 199 1 1 rF 94 199 200 1 rF 294 199 1 1 rF 295 199 200 1 rF 495 199 1 1 rF 495 199 1 1 rF 53 200 1 23 rF 93 200 1 23 rF 294 200 1 23 rF 495 200 1 23 rF 54 223 39 24 rC 59 245 :M f1_10 sf -.181(size)A gR gS 94 223 39 24 rC 99 245 :M f1_10 sf (2500)S gR gS 134 223 39 24 rC 140 245 :M f1_10 sf (1000)S gR gS 174 223 40 24 rC 180 245 :M f1_10 sf (500)S gR gS 215 223 39 24 rC 220 245 :M f1_10 sf (250)S gR gS 255 223 39 24 rC 260 245 :M f1_10 sf (100)S gR gS 295 223 39 24 rC 301 245 :M f1_10 sf (2500)S gR gS 335 223 40 24 rC 341 245 :M f1_10 sf (1000)S gR gS 376 223 39 24 rC 381 245 :M f1_10 sf (500)S gR gS 416 223 39 24 rC 421 245 :M f1_10 sf (250)S gR gS 456 223 39 24 rC 462 245 :M f1_10 sf (100)S gR gS 0 0 552 730 rC 53 223 1 1 rF 54 223 39 1 rF 93 223 1 1 rF 94 223 39 1 rF 133 223 1 1 rF 134 223 39 1 rF 173 223 1 1 rF 174 223 40 1 rF 214 223 1 1 rF 215 223 39 1 rF 254 223 1 1 rF 255 223 39 1 rF 294 223 1 1 rF 295 223 39 1 rF 334 223 1 1 rF 335 223 40 1 rF 375 223 1 1 rF 376 223 39 1 rF 415 223 1 1 rF 416 223 39 1 rF 455 223 1 1 rF 456 223 39 1 rF 495 223 1 1 rF 53 224 1 23 rF 93 224 1 23 rF 133 224 1 23 rF 173 224 1 23 rF 214 224 1 23 rF 254 224 1 23 rF 294 224 1 23 rF 334 224 1 23 rF 375 224 1 23 rF 415 224 1 23 rF 455 224 1 23 rF 495 224 1 23 rF 54 247 39 24 rC 59 269 :M f1_10 sf -.439(#a)A gR gS 94 247 39 24 rC 99 269 :M f1_10 sf (3)S gR gS 134 247 39 24 rC 140 269 :M f1_10 sf (3)S gR gS 174 247 40 24 rC 180 269 :M f1_10 sf (3)S gR gS 215 247 39 24 rC 220 269 :M f1_10 sf (3)S gR gS 255 247 39 24 rC 260 269 :M f1_10 sf (3)S gR gS 295 247 39 24 rC 301 269 :M f1_10 sf (1)S gR gS 335 247 40 24 rC 341 269 :M f1_10 sf (1)S gR gS 376 247 39 24 rC 381 269 :M f1_10 sf (1)S gR gS 416 247 39 24 rC 421 269 :M f1_10 sf .5(.6)A gR gS 456 247 39 24 rC 462 269 :M f1_10 sf .5(.6)A gR gS 0 0 552 730 rC 53 247 1 1 rF 54 247 39 1 rF 93 247 1 1 rF 94 247 39 1 rF 133 247 1 1 rF 134 247 39 1 rF 173 247 1 1 rF 174 247 40 1 rF 214 247 1 1 rF 215 247 39 1 rF 254 247 1 1 rF 255 247 39 1 rF 294 247 1 1 rF 295 247 39 1 rF 334 247 1 1 rF 335 247 40 1 rF 375 247 1 1 rF 376 247 39 1 rF 415 247 1 1 rF 416 247 39 1 rF 455 247 1 1 rF 456 247 39 1 rF 495 247 1 1 rF 53 248 1 23 rF 93 248 1 23 rF 133 248 1 23 rF 173 248 1 23 rF 214 248 1 23 rF 254 248 1 23 rF 294 248 1 23 rF 334 248 1 23 rF 375 248 1 23 rF 415 248 1 23 rF 455 248 1 23 rF 495 248 1 23 rF 54 271 39 24 rC 59 293 :M f1_10 sf -.602(%ac)A gR gS 94 271 39 24 rC 99 293 :M f1_10 sf (100)S gR gS 134 271 39 24 rC 140 293 :M f1_10 sf (100)S gR gS 174 271 40 24 rC 180 293 :M f1_10 sf (100)S gR gS 215 271 39 24 rC 220 293 :M f1_10 sf (100)S gR gS 255 271 39 24 rC 260 293 :M f1_10 sf (100)S gR gS 295 271 39 24 rC 301 293 :M f1_10 sf (100)S gR gS 335 271 40 24 rC 341 293 :M f1_10 sf (100)S gR gS 376 271 39 24 rC 381 293 :M f1_10 sf (20)S gR gS 416 271 39 24 rC 421 293 :M f1_10 sf (75)S gR gS 456 271 39 24 rC 462 293 :M f1_10 sf (100)S gR gS 0 0 552 730 rC 53 271 1 1 rF 54 271 39 1 rF 93 271 1 1 rF 94 271 39 1 rF 133 271 1 1 rF 134 271 39 1 rF 173 271 1 1 rF 174 271 40 1 rF 214 271 1 1 rF 215 271 39 1 rF 254 271 1 1 rF 255 271 39 1 rF 294 271 1 1 rF 295 271 39 1 rF 334 271 1 1 rF 335 271 40 1 rF 375 271 1 1 rF 376 271 39 1 rF 415 271 1 1 rF 416 271 39 1 rF 455 271 1 1 rF 456 271 39 1 rF 495 271 1 1 rF 53 272 1 23 rF 93 272 1 23 rF 133 272 1 23 rF 173 272 1 23 rF 214 272 1 23 rF 254 272 1 23 rF 294 272 1 23 rF 334 272 1 23 rF 375 272 1 23 rF 415 272 1 23 rF 455 272 1 23 rF 495 272 1 23 rF 54 295 39 24 rC 59 317 :M f1_10 sf -.219(#na)A gR gS 94 295 39 24 rC 99 317 :M f1_10 sf (11)S gR gS 134 295 39 24 rC 140 317 :M f1_10 sf (11)S gR gS 174 295 40 24 rC 180 317 :M f1_10 sf (11)S gR gS 215 295 39 24 rC 220 317 :M f1_10 sf (11)S gR gS 255 295 39 24 rC 260 317 :M f1_10 sf (11)S gR gS 295 295 39 24 rC 301 317 :M f1_10 sf (19)S gR gS 335 295 40 24 rC 341 317 :M f1_10 sf (19)S gR gS 376 295 39 24 rC 381 317 :M f1_10 sf (19)S gR gS 416 295 39 24 rC 421 317 :M f1_10 sf .167(12.4)A gR gS 456 295 39 24 rC 462 317 :M f1_10 sf .25(7.4)A gR gS 0 0 552 730 rC 53 295 1 1 rF 54 295 39 1 rF 93 295 1 1 rF 94 295 39 1 rF 133 295 1 1 rF 134 295 39 1 rF 173 295 1 1 rF 174 295 40 1 rF 214 295 1 1 rF 215 295 39 1 rF 254 295 1 1 rF 255 295 39 1 rF 294 295 1 1 rF 295 295 39 1 rF 334 295 1 1 rF 335 295 40 1 rF 375 295 1 1 rF 376 295 39 1 rF 415 295 1 1 rF 416 295 39 1 rF 455 295 1 1 rF 456 295 39 1 rF 495 295 1 1 rF 53 296 1 23 rF 93 296 1 23 rF 133 296 1 23 rF 173 296 1 23 rF 214 296 1 23 rF 254 296 1 23 rF 294 296 1 23 rF 334 296 1 23 rF 375 296 1 23 rF 415 296 1 23 rF 455 296 1 23 rF 495 296 1 23 rF 54 319 39 24 rC 59 341 :M f1_10 sf -.401(%nac)A gR gS 94 319 39 24 rC 99 341 :M f1_10 sf (100)S gR gS 134 319 39 24 rC 140 341 :M f1_10 sf (100)S gR gS 174 319 40 24 rC 180 341 :M f1_10 sf (100)S gR gS 215 319 39 24 rC 220 341 :M f1_10 sf (100)S gR gS 255 319 39 24 rC 260 341 :M f1_10 sf (100)S gR gS 295 319 39 24 rC 301 341 :M f1_10 sf (100)S gR gS 335 319 40 24 rC 341 341 :M f1_10 sf (100)S gR gS 376 319 39 24 rC 381 341 :M f1_10 sf (100)S gR gS 416 319 39 24 rC 421 341 :M f1_10 sf .167(98.3)A gR gS 456 319 39 24 rC 462 341 :M f1_10 sf .167(94.6)A gR gS 0 0 552 730 rC 53 319 1 1 rF 54 319 39 1 rF 93 319 1 1 rF 94 319 39 1 rF 133 319 1 1 rF 134 319 39 1 rF 173 319 1 1 rF 174 319 40 1 rF 214 319 1 1 rF 215 319 39 1 rF 254 319 1 1 rF 255 319 39 1 rF 294 319 1 1 rF 295 319 39 1 rF 334 319 1 1 rF 335 319 40 1 rF 375 319 1 1 rF 376 319 39 1 rF 415 319 1 1 rF 416 319 39 1 rF 455 319 1 1 rF 456 319 39 1 rF 495 319 1 1 rF 53 320 1 23 rF 53 343 1 1 rF 53 343 1 1 rF 54 343 39 1 rF 93 320 1 23 rF 93 343 1 1 rF 94 343 39 1 rF 133 320 1 23 rF 133 343 1 1 rF 134 343 39 1 rF 173 320 1 23 rF 173 343 1 1 rF 174 343 40 1 rF 214 320 1 23 rF 214 343 1 1 rF 215 343 39 1 rF 254 320 1 23 rF 254 343 1 1 rF 255 343 39 1 rF 294 320 1 23 rF 294 343 1 1 rF 295 343 39 1 rF 334 320 1 23 rF 334 343 1 1 rF 335 343 40 1 rF 375 320 1 23 rF 375 343 1 1 rF 376 343 39 1 rF 415 320 1 23 rF 415 343 1 1 rF 416 343 39 1 rF 455 320 1 23 rF 455 343 1 1 rF 456 343 39 1 rF 495 320 1 23 rF 495 343 1 1 rF 495 343 1 1 rF 265 354 :M f0_10 sf 3.159 .316(Table 1)J 243 370 :M .716(Bibliography)A 59 386 :M f1_10 sf -.041(Chickering, D. and Geiger, D. and Heckerman, D. \(1995\). Learning Bayesian networks: Search methods and)A 59 398 :M -.01(experimental results. Preliminary papers of the fifth international workshop on Artificial Intelligence and)A 59 410 :M .241 .024(Statistics, Fort Lauderdale, FL, pp. 112-128.)J 59 426 :M .341 .034(Pearl, J., \(1988\). Probabilistic Reasoning in Intelligent Systems, Morgan Kaufman: San Mateo, CA.)J 59 442 :M -.009(Pearl, J. \(1995\) Causal diagrams for empirical research, Biometrika, 82.)A 59 458 :M .029 .003(Raftery, A. \(1993\) Bayesian Model Selection in Structural Equation Models, in Testing )J 413 458 :M .037 .004(Structural )J 456 458 :M -.158(Equation)A 59 470 :M .221 .022(Models, ed. by K. Bollen and S. Long, Sage Publications.)J 59 486 :M -.049(Richardson, )A 112 486 :M .743 .074(T. )J 127 486 :M .074(\(1996)A f1_11 sf .12 .012(\). )J 163 486 :M .281 .028(A )J 178 486 :M .785 .078(discovery )J 229 486 :M 1.307 .131(algorithm )J 281 486 :M 1.099 .11(for )J 302 486 :M 1.017 .102(directed )J 346 486 :M .619 .062(cyclic )J 380 486 :M 1.282 .128(graphs. )J 421 486 :M 1.111 .111(Uncertainty )J 482 486 :M .444(in)A 59 497 :M .822 .082(Artificial Intelligence, Proceedings, 12th Conference, Morgan Kaufman, CA.)J 59 514 :M f1_10 sf .683 .068(Spirtes, )J 94 514 :M 1.493 .149(P., )J 110 514 :M .498 .05(Glymour, )J 153 514 :M 1.408 .141(C., )J 170 514 :M -.313(and )A 187 514 :M .241 .024(Scheines, )J 229 514 :M 1.408 .141(R., )J 246 514 :M -.026(\(1993\) )A 277 514 :M .504 .05(Causation, )J 325 514 :M -.009(Prediction, )A 373 514 :M -.313(and )A 391 514 :M -.029(Search, )A 425 514 :M -.153(\(Springer-Verlag)A 59 526 :M .149 .015(Lecture Notes in Statistics 81, New York\).)J 59 542 :M .683 .068(Spirtes, )J 94 542 :M 1.493 .149(P., )J 110 542 :M -.049(Richardson, )A 162 542 :M 1.07 .107(T., )J 179 542 :M .156 .016(Meek, )J 209 542 :M 1.408 .141(C., )J 227 542 :M .241 .024(Scheines, )J 270 542 :M 1.408 .141(R., )J 288 542 :M -.313(and )A 306 542 :M .498 .05(Glymour, )J 350 542 :M 1.108 .111(C. )J 365 542 :M .203 .02(\(1996\). )J 399 542 :M .409 .041(Using )J 428 542 :M -.095(D-separation )A 483 542 :M .222(to)A 59 554 :M -.029(Calculate )A 100 554 :M -.094(Zero )A 122 554 :M .236 .024(Partial )J 152 554 :M .033 .003(Correlations )J 205 554 :M .601 .06(in )J 217 554 :M -.099(Linear )A 246 554 :M -.083(Models )A 279 554 :M .517 .052(with )J 301 554 :M -.17(Correlated )A 345 554 :M (Errors, )S 376 554 :M -.074(Carnegie )A 415 554 :M .385 .038(Mellon )J 449 554 :M -.023(University)A 59 566 :M .096 .01(Technical Report Phil-72.)J 59 582 :M .683 .068(Spirtes, )J 94 582 :M 1.493 .149(P., )J 110 582 :M -.313(and )A 127 582 :M .156 .016(Meek, )J 156 582 :M 1.108 .111(C. )J 170 582 :M .203 .02(\(1995\). )J 204 582 :M -.074(Learning )A 244 582 :M -.144(Bayesian )A 284 582 :M -.046(Networks )A 327 582 :M .517 .052(with )J 350 582 :M -.101(Discrete )A 387 582 :M -.09(Variables )A 429 582 :M .047 .005(from )J 453 582 :M (Data", )S 483 582 :M .222(in)A 59 594 :M -.038(Proceedings of The First International Conference on Knowledge Discovery and Data Mining, ed. by )A 464 594 :M -.191(Usama)A 59 606 :M .123 .012(M. Fayyad and Ramasamy Uthurusamy, AAI Press, pp. 294-299.)J 59 622 :M .206 .021(Wright, S. \(1934\). The method of path coefficients. Annals of Mathematical Statistics, 5, 161-215.)J endp %%Trailer end %%EOF