%!PS-Adobe-3.0 %%Title: (Microsoft Word - freedman2a) %%Creator: (Microsoft Word: LaserWriter 8 8.3.4) %%CreationDate: (12:02 AM Wednesday, March 26, 1997) %%For: (peter) %%Pages: 25 %%DocumentFonts: Times-Bold Times-Roman Times-Italic Symbol %%DocumentNeededFonts: Times-Bold Times-Roman Times-Italic Symbol %%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 - freedman2a)def /Creator(Microsoft Word: LaserWriter 8 8.3.4)def /CreationDate(12:02 AM Wednesday, March 26, 1997)def /For(peter)def /Pages 25 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 211 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_NON-uniform_graphics %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /@d { gS np :M 1 index 0 rl 0 exch rl neg 0 rl :K scale 1 lw stroke gR }bd /oh Z /ow Z /y2 Z /y1 Z /x2 Z /x1 Z /rad Z /ph Z /pw Z /arct where { pop }{ /arct { arcto pop pop pop pop }bd }ifelse /@r { /oh xs /ow xs oh div /y2 xs ow div /x2 xs oh div /y1 xs ow div /x1 xs gS np ow oh scale x2 x1 add 2 div y1 :M x2 y1 x2 y2 .5 arct x2 y2 x1 y2 .5 arct x1 y2 x1 y1 .5 arct x1 y1 x2 y1 .5 arct fill gR }bd /@t { /rad xs /y2 xs /x2 xs /y1 xs /x1 xs gS 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 scale 1 lw stroke gR }bd /@u { /oh xs /ow xs /ph xs /pw xs oh div /y2 xs ow div /x2 xs oh div /y1 xs ow div /x1 xs gS np $m currentmatrix ow oh scale x2 x1 add 2 div y1 :M x2 y1 x2 y2 .5 arct x2 y2 x1 y2 .5 arct x1 y2 x1 y1 .5 arct x1 y1 x2 y1 .5 arct :K setmatrix pw ph scale 1 lw stroke gR }bd /@g { gS np 0 360 arc :K scale 1 lw stroke gR }bd /@h { gS np $m currentmatrix pop :T scale 0 0 .5 0 360 arc $m setmatrix scale 1 lw :K stroke gR }bd /@o { gS np arc scale 1 lw stroke gR }bd /@p { gS np $m currentmatrix pop :T scale 0 0 .5 5 -2 roll arc $m setmatrix scale 1 lw stroke gR }bd %%EndFile %%BeginFile: adobe_psp_basic_text %%Copyright: Copyright 1990-1993 Adobe Systems Incorporated. All Rights Reserved. /S/show ld /A{ 0.0 exch ashow }bd /R{ 0.0 exch 32 exch widthshow }bd /W{ 0.0 3 1 roll widthshow }bd /J{ 0.0 32 4 2 roll 0.0 exch awidthshow }bd /V{ 0.0 4 1 roll 0.0 exch awidthshow }bd /fcflg true def /fc{ fcflg{ vmstatus exch sub 50000 lt{ (%%[ Warning: Running out of memory ]%%\r)print flush/fcflg false store }if pop }if }bd /$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: Symbol /f0_1/Times-Bold :mre /f0_12 f0_1 12 scf /f1_1/Times-Roman :mre /f1_12 f1_1 12 scf /f1_10 f1_1 10 scf /f2_1/Times-Italic :mre /f2_12 f2_1 12 scf /f2_10 f2_1 10 scf /f3_1/Symbol :bsr 240/apple pd :esr /f3_12 f3_1 12 scf /f4_1 f3_1 :mi /f4_12 f4_1 12 scf /Courier findfont[10 0 0 -10 0 0]:mf setfont %%EndSetup %%Page: 1 1 %%BeginPageSetup initializepage (peter; page: 1 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 221 50 :M f0_12 sf 2.325 .232(Reply to Freedman)J 185 74 :M f1_12 sf -.082(by Peter Spirtes and Richard Scheines)A 59 122 :M (In )S 76 122 :M (Causation, )S 134 122 :M -.029(Prediction, )A 193 122 :M -.109(and )A 218 122 :M -.107(Search )A 258 122 :M .359 .036(\(Spirtes, )J 307 122 :M .375 .038(Glymour, )J 362 122 :M -.109(and )A 387 122 :M -.081(Scheines )A 437 122 :M .629 .063(1993\), )J 477 122 :M (we)S 59 146 :M -.073(undertook )A 112 146 :M -.326(a )A 122 146 :M -.196(three )A 150 146 :M -.163(part )A 173 146 :M -.039(project. )A 214 146 :M -.087(\(Henceforth )A 276 146 :M (we )S 295 146 :M -.166(will )A 318 146 :M -.126(refer )A 345 146 :M -.167(to )A 359 146 :M (Causation, )S 416 146 :M -.029(Prediction, )A 474 146 :M -.163(and)A 59 170 :M -.107(Search )A 96 170 :M (as )S 111 170 :M 1.107 .111(CPS.\) )J 147 170 :M .626 .063(First, )J 179 170 :M (we )S 199 170 :M -.226(characterized )A 266 170 :M (when )S 298 170 :M -.163(causal )A 333 170 :M -.11(models )A 373 170 :M -.215(are )A 393 170 :M -.117(indistinguishable )A 479 170 :M (by)S 59 194 :M -.133(population )A 113 194 :M -.181(conditional )A 169 194 :M -.164(independence )A 237 194 :M -.146(relations )A 281 194 :M -.064(under )A 312 194 :M -.139(several )A 349 194 :M -.144(different )A 393 194 :M -.03(assumptions )A 456 194 :M -.235(relating)A 59 218 :M -.08(causality to probability. Second, we proposed a number of algorithms that take )A 435 218 :M -.165(sample )A 472 218 :M -.329(data)A 59 242 :M -.109(and )A 82 242 :M -.166(optional )A 127 242 :M -.065(background )A 190 242 :M -.072(knowledge )A 249 242 :M (as )S 266 242 :M .208 .021(input, )J 301 242 :M -.109(and )A 325 242 :M -.111(output )A 362 242 :M -.326(a )A 374 242 :M f2_12 sf -.177(class)A f1_12 sf ( )S 404 242 :M (of )S 421 242 :M -.163(causal )A 457 242 :M -.132(models)A 59 266 :M -.125(compatible with the data and the background knowledge; the algorithms \(with the )A 446 266 :M -.206(exception)A 59 290 :M (of )S 73 290 :M -.22(the )A 91 290 :M -.146(heuristic )A 135 290 :M -.184(algorithm )A 184 290 :M -.108(described )A 233 290 :M -.167(in )A 246 290 :M -.141(Chapter )A 287 290 :M (11\) )S 308 290 :M -.077(were )A 336 290 :M -.209(accompanied )A 402 290 :M (by )S 419 290 :M .217 .022(proofs )J 455 290 :M (of )S 470 290 :M -.247(their)A 59 314 :M -.087(correctness )A 117 314 :M -.132(given )A 148 314 :M -.03(assumptions )A 212 314 :M -.249(that )A 234 314 :M -.077(were )A 262 314 :M -.234(clearly )A 298 314 :M -.165(stated )A 330 314 :M -.167(in )A 344 314 :M 1.182 .118(CPS, )J 375 314 :M -.109(and )A 397 314 :M -.249(that )A 419 314 :M (we )S 438 314 :M -.166(will )A 461 314 :M -.218(restate)A 59 338 :M -.014(below. Finally, we offered a theory of how )A 268 338 :M -.167(to )A 281 338 :M -.188(predict )A 317 338 :M -.22(the )A 335 338 :M -.138(effects )A 370 338 :M (of )S 384 338 :M -.127(interventions )A 449 338 :M -.167(in )A 462 338 :M -.196(causal)A 59 362 :M -.076(structures, given only partial )A 198 362 :M -.072(knowledge )A 254 362 :M (of )S 268 362 :M -.163(causal )A 301 362 :M (structure. )S 350 362 :M .598 .06(Freedman's )J 410 362 :M -.132(objections )A 462 362 :M -.215(are )A 480 362 :M -.497(all)A 59 386 :M -.103(directed against the causal inference algorithms we proposed. We do not have )A 429 386 :M -.082(room )A 458 386 :M -.161(here )A 482 386 :M -.334(to)A 59 410 :M .199 .02(discuss )J 98 410 :M -.331(all )A 113 410 :M (of )S 127 410 :M (his )S 145 410 :M -.059(criticisms, )A 198 410 :M -.111(but )A 217 410 :M (we )S 235 410 :M -.163(have )A 261 410 :M -.038(answered )A 311 410 :M (his )S 330 410 :M -.197(major )A 362 410 :M .391 .039(points. )J 400 410 :M -.249(With )A 428 410 :M -.106(regard )A 463 410 :M -.167(to )A 477 410 :M -.33(the)A 59 434 :M -.036(points we )A 109 434 :M (do )S 125 434 :M -.111(not )A 144 434 :M -.163(have )A 170 434 :M -.082(room )A 199 434 :M -.167(to )A 212 434 :M .744 .074(discuss, )J 255 434 :M -.22(the )A 273 434 :M -.161(reader )A 306 434 :M (should )S 342 434 :M -.163(be )A 357 434 :M -.051(warned )A 396 434 :M -.249(that )A 417 434 :M -.122(Freedman )A 468 434 :M (is )S 480 434 :M -.326(an)A 59 458 :M -.197(unreliable )A 112 458 :M -.178(interpreter )A 167 458 :M (of )S 184 458 :M -.081(what )A 214 458 :M (we )S 235 458 :M -.163(have )A 264 458 :M (written. )S 309 458 :M .258 .026(For )J 334 458 :M -.08(convenience, )A 404 458 :M (we )S 426 458 :M -.163(have )A 456 458 :M -.166(divided)A 59 482 :M -.054(Freedman's objections into the following categories.)A 59 506 :M .775 .077(1.\) )J 77 506 :M -.122(Freedman )A 128 506 :M -.036(questions )A 177 506 :M -.082(some )A 206 506 :M (of )S 220 506 :M -.22(the )A 238 506 :M -.03(assumptions )A 301 506 :M (on )S 317 506 :M -.065(which )A 350 506 :M (our )S 371 506 :M -.087(correctness )A 429 506 :M -.123(theorems )A 477 506 :M -.323(are)A 59 530 :M .113 .011(based. Some )J 124 530 :M (of )S 138 530 :M (his )S 156 530 :M -.165(criticisms )A 205 530 :M -.215(are )A 223 530 :M -.064(based )A 254 530 :M (on )S 270 530 :M -.196(covariance )A 324 530 :M -.205(matrices )A 367 530 :M -.249(that )A 388 530 :M -.163(he )A 403 530 :M -.026(constructed. )A 465 530 :M (None)S 59 554 :M -.054(of the examples he constructed in sections 11.2, )A 290 554 :M 1.333 .133(11.3, )J 320 554 :M (or )S 334 554 :M .714 .071(12.3 )J 360 554 :M -.215(are )A 378 554 :M -.153(counterexamples )A 461 554 :M -.167(to )A 474 554 :M -.163(any)A 59 578 :M -.103(theorem that we stated, nor are they even )A 256 578 :M -.186(germane )A 300 578 :M -.167(to )A 313 578 :M -.22(the )A 331 578 :M -.083(question )A 375 578 :M (of )S 389 578 :M .259 .026(how )J 414 578 :M -.122(probable )A 459 578 :M -.215(are )A 477 578 :M -.33(the)A 59 602 :M -.015(assumptions we make. )A 171 602 :M .258 .026(His )J 192 602 :M -.164(examples )A 240 602 :M -.083(only )A 265 602 :M -.198(illustrate )A 309 602 :M -.056(points )A 342 602 :M (discussed )S 392 602 :M -.167(in )A 405 602 :M -.276(detail )A 434 602 :M -.167(in )A 447 602 :M (our )S 467 602 :M (book)S 59 626 :M -.104(\(particularly in the chapter on indistinguishability\), in which we give similar examples.)A 59 650 :M .775 .077(2.\) )J 77 650 :M -.219(The )A 99 650 :M -.084(most )A 126 650 :M (serious )S 164 650 :M -.162(charge )A 199 650 :M -.249(that )A 220 650 :M -.122(Freedman )A 271 650 :M -.131(makes )A 305 650 :M (is )S 318 650 :M -.249(that )A 340 650 :M -.22(the )A 359 650 :M -.132(algorithms )A 414 650 :M (do )S 431 650 :M -.111(not )A 451 650 :M -.22(compute)A 59 674 :M -.077(what we say they do. According to Freedman:)A endp %%Page: 2 2 %%BeginPageSetup initializepage (peter; page: 2 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 77 74 :M f1_12 sf .122 .012(SGS seem )J 131 74 :M -.167(to )A 144 74 :M -.331(claim )A 173 74 :M -.249(that )A 194 74 :M -.197(their )A 219 74 :M -.132(algorithms )A 273 74 :M -.166(will )A 295 74 :M -.082(find )A 318 74 :M -.331(all )A 333 74 :M -.22(the )A 351 74 :M -.165(path )A 375 74 :M -.123(diagrams )A 422 74 :M -.257(compatible)A 77 98 :M -.073(with a given covariance matrix. However, the )A 297 98 :M -.123(theorems )A 344 98 :M (suggest )S 384 98 :M -.249(that )A 405 98 :M -.22(the )A 423 98 :M -.147(algorithms)A 77 122 :M -.166(will )A 99 122 :M -.33(at )A 111 122 :M -.082(best )A 134 122 :M -.082(find )A 157 122 :M -.109(one )A 178 122 :M (such )S 204 122 :M .425 .043(graph. )J 239 122 :M .765 .077(SGS )J 266 122 :M -.082(also )A 289 122 :M -.163(seem )A 317 122 :M -.167(to )A 330 122 :M -.331(claim )A 359 122 :M -.249(that )A 380 122 :M -.197(their )A 405 122 :M -.132(algorithms )A 459 122 :M -.323(are)A 77 146 :M (consistent. )S 134 146 :M .571 .057(However, )J 188 146 :M -.095(without )A 230 146 :M -.163(an )A 248 146 :M -.221(identifiability )A 317 146 :M -.109(theory )A 354 146 :M (for )S 375 146 :M -.219(linear )A 408 146 :M .199 .02(models, )J 453 146 :M -.22(they)A 77 170 :M -.065(cannot be talking about consistency. \(Freedman, 49\))A 59 218 :M -.071(Freedman's claim that our algorithms do not find )A 294 218 :M -.331(all )A 309 218 :M (of )S 323 218 :M -.22(the )A 341 218 :M -.165(path )A 365 218 :M -.123(diagrams )A 412 218 :M -.191("compatible")A 59 242 :M -.128(\(in a sense explained in detail below\) with a given covariance matrix is )A 395 242 :M .221 .022(false, )J 425 242 :M -.109(and )A 446 242 :M -.08(based)A 59 266 :M -.106(on a fundamental misunderstanding of the output of the algorithms )A 377 266 :M -.109(and )A 398 266 :M -.22(the )A 416 266 :M -.123(theorems )A 463 266 :M (of)S 59 290 :M (correctness.)S 59 338 :M .775 .077(3.\) )J 77 338 :M (Finally, )S 118 338 :M -.122(Freedman )A 169 338 :M -.22(claims )A 203 338 :M (our )S 224 338 :M -.256(empirical )A 272 338 :M -.062(cases )A 302 338 :M (our )S 323 338 :M -.025(unconvincing. )A 396 338 :M (He )S 415 338 :M -.052(raises )A 447 338 :M -.22(many)A 59 362 :M -.12(substantive objections to a number of the models of real data that )A 368 362 :M -.077(were )A 395 362 :M -.108(presented )A 444 362 :M -.167(in )A 457 362 :M (our)S 59 386 :M -.068(book. What we said about these examples was:)A 77 434 :M -.132(We illustrate the algorithms for simulated and real data sets. With simulated )A 436 434 :M -.247(data )A 459 434 :M -.33(the)A 77 458 :M -.133(examples illustrate the properties of )A 248 458 :M -.22(the )A 266 458 :M -.132(algorithms )A 320 458 :M (on )S 336 458 :M -.093(samples )A 378 458 :M (of )S 392 458 :M -.219(realistic )A 432 458 :M .425 .042(sizes. )J 463 458 :M (In)S 77 482 :M -.098(the empirical cases we often do not know )A 276 482 :M -.092(whether )A 318 482 :M -.163(an )A 333 482 :M -.184(algorithm )A 382 482 :M -.039(produces )A 429 482 :M -.22(the )A 447 482 :M .068(truth.)A 77 506 :M -.151(But it is at the least )A 170 506 :M -.08(very )A 195 506 :M -.15(interesting )A 248 506 :M -.249(that )A 269 506 :M -.167(in )A 282 506 :M -.062(cases )A 311 506 :M -.167(in )A 324 506 :M -.065(which )A 357 506 :M -.101(investigators )A 421 506 :M -.163(have )A 447 506 :M -.165(given)A 77 530 :M -.132(some care to the treatment and explanation of their data, the algorithm reproduces )A 463 530 :M (or)S 77 554 :M -.163(nearly )A 110 554 :M -.063(reproduces )A 166 554 :M -.22(the )A 184 554 :M -.073(published )A 234 554 :M -.122(accounts )A 279 554 :M (of )S 293 554 :M -.163(causal )A 326 554 :M -.031(relations. )A 375 554 :M -.164(It )A 387 554 :M (is )S 400 554 :M -.082(also )A 424 554 :M -.165(interesting)A 77 578 :M -.249(that )A 103 578 :M -.167(in )A 121 578 :M -.062(cases )A 155 578 :M -.095(without )A 200 578 :M -.131(these )A 233 578 :M -.093(virtues )A 274 578 :M -.22(the )A 297 578 :M -.184(algorithm )A 351 578 :M .188 .019(suggests )J 401 578 :M -.199(quite )A 433 578 :M -.163(different)A 77 602 :M -.137(explanations )A 141 602 :M -.08(from )A 169 602 :M -.065(those )A 199 602 :M -.182(advocated )A 251 602 :M -.167(in )A 265 602 :M -.073(published )A 316 602 :M .381 .038(reports. )J 358 602 :M .359 .036(\(Spirtes, )J 404 602 :M .375 .038(Glymour, )J 456 602 :M -.163(and)A 77 626 :M .317 .032(Scheines 1993, 132-133.\))J endp %%Page: 3 3 %%BeginPageSetup initializepage (peter; page: 3 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.075(Freedman's substantive criticisms of the models produced do not in any way contradict )A 474 50 :M -.112(this)A 59 74 :M -.131(claim.)A 59 98 :M -.084(Freedman's criticisms are marred by some fundamental )A 324 98 :M -.146(misinterpretations )A 412 98 :M (of )S 426 98 :M -.081(what )A 453 98 :M (we )S 471 98 :M .336(say.)A 59 122 :M -.331(On )A 77 122 :M -.163(more )A 105 122 :M -.165(than )A 130 122 :M -.109(one )A 152 122 :M -.122(occasion )A 198 122 :M -.163(he )A 214 122 :M -.23(criticizes )A 260 122 :M -.081(what )A 288 122 :M (we )S 307 122 :M -.074("seem" )A 346 122 :M -.167(to )A 360 122 :M .719 .072(say, )J 385 122 :M -.163(even )A 412 122 :M -.056(though )A 450 122 :M (we )S 469 122 :M -.217(have)A 59 146 :M -.129(never )A 89 146 :M -.165(held )A 113 146 :M (or )S 127 146 :M -.165(stated )A 158 146 :M -.22(the )A 176 146 :M -.084(position )A 218 146 :M -.163(he )A 233 146 :M -.165(attributes )A 280 146 :M -.167(to )A 293 146 :M 1.025 .103(us. )J 312 146 :M -.328(Of )A 328 146 :M -.22(the )A 346 146 :M (few )S 368 146 :M -.219(direct )A 398 146 :M -.1(quotations )A 452 146 :M -.08(from )A 480 146 :M .333(us)A 59 170 :M -.249(that )A 80 170 :M -.163(he )A 95 170 :M .421 .042(gives, )J 128 170 :M (two )S 150 170 :M -.215(are )A 168 170 :M -.197(taken )A 197 170 :M -.111(out )A 216 170 :M (of )S 230 170 :M -.189(context )A 268 170 :M (\(Freedman, )S 328 170 :M (24 )S 345 170 :M -.109(and )A 367 170 :M .719 .072(25\). )J 392 170 :M (In )S 407 170 :M -.109(one )A 429 170 :M (of )S 444 170 :M -.131(these )A 473 170 :M (two)S 59 194 :M -.078(quotations, Freedman replaces )A 207 194 :M -.109(key )A 228 194 :M -.131(qualifiers )A 276 194 :M -.065(which )A 309 194 :M -.231(completely )A 364 194 :M -.163(change )A 401 194 :M -.22(the )A 419 194 :M -.189(meaning )A 463 194 :M (of )S 477 194 :M -.33(the)A 59 218 :M -.06(quotation with "****", and remarks that "Readers )A 302 218 :M -.22(may )A 326 218 :M -.094(consult )A 364 218 :M -.22(the )A 382 218 :M -.165(original )A 422 218 :M (for )S 440 218 :M -.04(context, )A 482 218 :M -.334(to)A 59 242 :M -.106(see )A 80 242 :M -.092(whether )A 124 242 :M -.22(the )A 144 242 :M -.237(omitted )A 185 242 :M -.288(material )A 228 242 :M -.138(affects )A 265 242 :M -.22(the )A 285 242 :M -.024(meaning." )A 340 242 :M (\(Freedman, )S 401 242 :M (24\) )S 423 242 :M -.262(Later )A 453 242 :M (we )S 473 242 :M -.222(will)A 59 266 :M -.123(produce the full )A 137 266 :M -.132(quote )A 167 266 :M .277 .028(so )J 182 266 :M -.249(that )A 203 266 :M -.09(readers )A 241 266 :M -.166(will )A 263 266 :M -.163(be )A 278 266 :M -.247(able )A 301 266 :M -.167(to )A 314 266 :M -.106(see )A 333 266 :M .259 .026(how )J 358 266 :M -.22(the )A 376 266 :M -.237(omitted )A 415 266 :M -.288(material )A 456 266 :M -.109(and )A 477 266 :M -.33(the)A 59 290 :M -.121(context affects the meaning.)A 59 314 :M f0_12 sf 2.436 .244(1. The PC Algorithm)J 59 338 :M f1_12 sf -.052(A number of Freedman's objections are based on )A 295 338 :M -.058(misunderstandings )A 388 338 :M (of )S 402 338 :M -.22(the )A 420 338 :M -.132(algorithms )A 474 338 :M -.331(that)A 59 362 :M -.072(we proposed and their accompanying correctness theorems. Hence, it will be useful )A 458 362 :M -.167(to )A 471 362 :M -.22(give)A 59 386 :M -.129(brief )A 86 386 :M -.082(descriptions )A 148 386 :M (of )S 163 386 :M -.22(the )A 183 386 :M -.132(algorithms )A 239 386 :M -.109(and )A 262 386 :M -.22(the )A 282 386 :M -.087(correctness )A 341 386 :M -.123(theorems )A 390 386 :M .236 .024(here. )J 420 386 :M -.131(Since )A 452 386 :M -.084(most )A 481 386 :M (of)S 59 410 :M -.031(Freedman's objections are )A 187 410 :M -.205(directed )A 228 410 :M -.141(against )A 265 410 :M -.22(the )A 283 410 :M .271 .027(PC )J 302 410 :M -.066(algorithm, )A 355 410 :M -.249(that )A 376 410 :M (is )S 388 410 :M -.22(the )A 406 410 :M -.184(algorithm )A 455 410 :M (we )S 473 410 :M -.222(will)A 59 434 :M -.063(discuss in the most detail.)A 59 458 :M -.663(A )A 72 458 :M -.205(directed )A 114 458 :M -.282(acyclic )A 151 458 :M -.064(graph )A 183 458 :M -.195(\(DAG\) )A 221 458 :M -.217(can )A 242 458 :M -.163(be )A 258 458 :M (used )S 285 458 :M -.167(to )A 299 458 :M -.107(represent )A 347 458 :M (two )S 370 458 :M -.166(distinct )A 409 458 :M -.065(types )A 439 458 :M (of )S 454 458 :M (objects.)S 59 482 :M -.068(First, it can be used to represent a set of probability distributions, all of )A 398 482 :M -.065(which )A 431 482 :M -.062(share )A 460 482 :M -.273(certain)A 59 506 :M -.165(conditional independence )A 182 506 :M -.146(relations )A 226 506 :M -.167(in )A 239 506 :M (common. )S 288 506 :M .398 .04(Second, )J 331 506 :M -.334(it )A 341 506 :M -.217(can )A 361 506 :M -.163(be )A 376 506 :M (used )S 402 506 :M -.167(to )A 415 506 :M -.107(represent )A 462 506 :M -.196(causal)A 59 530 :M -.101(relationships )A 123 530 :M -.139(between )A 166 530 :M -.164(variables; )A 215 530 :M -.132(given )A 245 530 :M -.326(a )A 254 530 :M -.164(causally )A 297 530 :M -.131(sufficient )A 346 530 :M -.109(set )A 364 530 :M (of )S 379 530 :M -.145(variables )A 426 530 :M f0_12 sf .25(V)A f1_12 sf .087 .009( )J 440 530 :M .898 .09(\(i.e. )J 465 530 :M -.161(every)A 59 554 :M -.033(common cause of variables in )A f0_12 sf -.057(V)A f1_12 sf -.027( is also in )A f0_12 sf -.057(V)A f1_12 sf -.03(\), there is an edge from )A f2_12 sf (X)S f1_12 sf -.025( to )A f2_12 sf (Y)S f1_12 sf -.025( in )A f2_12 sf -.057(G)A f1_12 sf -.033( if and only)A 59 578 :M -.164(if )A 71 578 :M f2_12 sf 1.185(X)A f1_12 sf .485 .048( )J 85 578 :M (is )S 98 578 :M -.326(a )A 108 578 :M -.219(direct )A 139 578 :M -.129(cause )A 170 578 :M (of )S 185 578 :M f2_12 sf .917(Y)A f1_12 sf .412 .041( )J 198 578 :M -.247(relative )A 237 578 :M -.167(to )A 251 578 :M f0_12 sf .79(V)A f1_12 sf .497 .05(. )J 269 578 :M -.326(We )A 290 578 :M -.33(call )A 311 578 :M -.164(DAGs )A 346 578 :M -.179(interpreted )A 401 578 :M -.167(in )A 415 578 :M -.084(this )A 437 578 :M (way )S 462 578 :M -.196(causal)A 59 602 :M -.074(DAGs. These two distinct uses of DAGs can be linked by the following assumptions:)A 77 650 :M f0_12 sf .607 .061(Causal Markov Condition: )J f1_12 sf .321 .032(Let )J f2_12 sf .205(G)A f1_12 sf .35 .035( be a causal DAG with vertex )J 399 650 :M -.109(set )A 416 650 :M f0_12 sf .25(V)A f1_12 sf .087 .009( )J 429 650 :M -.109(and )A 450 650 :M f2_12 sf .475(P)A f0_12 sf .195 .019( )J 462 650 :M f1_12 sf -.326(be)A 77 674 :M -.326(a )A 86 674 :M -.15(probability )A 141 674 :M -.111(distribution )A 199 674 :M -.08(over )A 224 674 :M -.22(the )A 242 674 :M -.163(vertices )A 283 674 :M -.167(in )A 297 674 :M f0_12 sf 1.215 .122(V )J 312 674 :M f1_12 sf -.181(generated )A 362 674 :M (by )S 379 674 :M -.22(the )A 398 674 :M -.163(causal )A 432 674 :M -.122(structure)A endp %%Page: 4 4 %%BeginPageSetup initializepage (peter; page: 4 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 77 50 :M f1_12 sf .08 .008(represented by )J f2_12 sf (G)S f1_12 sf (. )S f2_12 sf (G)S f1_12 sf ( )S 178 50 :M -.109(and )A 199 50 :M f2_12 sf -.234(P)A f1_12 sf ( )S 210 50 :M -.046(satisfy )A 245 50 :M -.22(the )A 263 50 :M -.11(Causal )A 299 50 :M -.164(Markov )A 340 50 :M -.112(Condition )A 391 50 :M -.164(if )A 402 50 :M -.109(and )A 423 50 :M -.083(only )A 448 50 :M -.164(if )A 459 50 :M (for)S 77 73 :M -.129(every )A 107 73 :M f2_12 sf .774(W)A f1_12 sf .232 .023( )J 122 73 :M -.167(in )A 135 73 :M f0_12 sf .79(V)A f1_12 sf .497 .05(, )J 152 73 :M f2_12 sf .774(W)A f1_12 sf .232 .023( )J 167 73 :M (is )S 179 73 :M -.15(independent )A 240 73 :M (of )S 254 73 :M f0_12 sf .605(V)A f1_12 sf .256<5C28>A f0_12 sf .406(Descendants)A f1_12 sf .279<28>A f2_12 sf .698(W)A f1_12 sf .444 .044(\) )J 363 73 :M f3_12 sf -.161A f1_12 sf ( )S 377 73 :M f0_12 sf .324(Parents)A f1_12 sf .231<28>A f2_12 sf .577(W)A f1_12 sf .529 .053(\)\) )J 447 73 :M -.165(given)A 77 98 :M f0_12 sf .438(Parents)A f1_12 sf .312<28>A f2_12 sf .78(W)A f1_12 sf .546(\).)A 77 122 :M f0_12 sf .49 .049(Faithfulness Condition: )J f1_12 sf .236 .024(Let )J f2_12 sf .151(G)A f1_12 sf .232 .023( be a causal DAG and )J f2_12 sf .128(P)A f1_12 sf .38 .038( a probability distribution)J 77 146 :M -.181(generated )A 126 146 :M (by )S 142 146 :M f2_12 sf .79(G)A f1_12 sf .497 .05(. )J 159 146 :M .496(<)A f2_12 sf .634(G)A f1_12 sf .399 .04(, )J 183 146 :M f2_12 sf (P)S f1_12 sf -.056(> )A 201 146 :M -.072(satisfies )A 243 146 :M -.22(the )A 261 146 :M -.054(Faithfulness )A 323 146 :M -.112(Condition )A 375 146 :M -.164(if )A 387 146 :M -.109(and )A 409 146 :M -.083(only )A 435 146 :M -.164(if )A 447 146 :M -.161(every)A 77 170 :M -.181(conditional )A 135 170 :M -.164(independence )A 205 170 :M -.206(relation )A 246 170 :M -.163(true )A 270 170 :M -.167(in )A 285 170 :M f2_12 sf -.234(P)A f1_12 sf ( )S 299 170 :M (is )S 314 170 :M -.248(entailed )A 357 170 :M (by )S 376 170 :M -.22(the )A 397 170 :M -.11(Causal )A 436 170 :M -.197(Markov)A 77 194 :M -.057(Condition applied to )A f2_12 sf -.101(G)A f1_12 sf (.)S 59 242 :M -.177(Their meaning )A 131 242 :M -.109(and )A 152 242 :M -.178(justification )A 211 242 :M -.215(are )A 229 242 :M (discussed )S 279 242 :M -.163(more )A 307 242 :M -.132(fully )A 333 242 :M -.167(in )A 346 242 :M -.046(Glymour )A 393 242 :M -.066(\(this )A 418 242 :M -.141(volume\) )A 461 242 :M -.109(and )A 482 242 :M -.334(in)A 59 266 :M 1.182 .118(CPS. )J 89 266 :M .571 .057(However, )J 141 266 :M -.164(if )A 152 266 :M -.109(one )A 173 266 :M -.131(makes )A 207 266 :M -.131(these )A 235 266 :M .305 .03(assumptions, )J 302 266 :M -.165(then )A 326 266 :M -.22(the )A 344 266 :M -.15(probability )A 399 266 :M -.111(distribution )A 457 266 :M (of )S 472 266 :M -.329(data)A 59 290 :M -.181(generated )A 108 290 :M (by )S 124 290 :M -.326(a )A 134 290 :M -.163(causal )A 168 290 :M (process )S 209 290 :M -.117(represented )A 268 290 :M (by )S 285 290 :M -.163(causal )A 319 290 :M -.33(DAG )A 349 290 :M f2_12 sf .25(G)A f1_12 sf .087 .009( )J 363 290 :M (is )S 376 290 :M -.326(a )A 386 290 :M -.219(member )A 429 290 :M (of )S 444 290 :M -.22(the )A 463 290 :M -.109(set )A 481 290 :M (of)S 59 314 :M -.06(probability distributions represented by )A f2_12 sf -.111(G)A f1_12 sf (.)S 59 338 :M -.125(Sometimes different DAGs represent )A 237 338 :M -.22(the )A 255 338 :M -.163(same )A 283 338 :M -.109(set )A 300 338 :M (of )S 314 338 :M -.15(probability )A 369 338 :M (distributions. )S 436 338 :M (In )S 450 338 :M -.249(that )A 471 338 :M -.215(case)A 59 362 :M -.075(we say that the two DAGs are faithfully indistinguishable. \(In CPS we define two DAGs as)A 59 386 :M -.165(faithfully )A 108 386 :M -.117(indistinguishable )A 194 386 :M (when )S 226 386 :M -.165(they )A 252 386 :M -.276(entail )A 283 386 :M -.22(the )A 303 386 :M -.163(same )A 333 386 :M -.109(set )A 352 386 :M (of )S 368 386 :M -.181(conditional )A 427 386 :M -.179(independence)A 59 410 :M -.126(relations. But if they entail the same set of conditional independence relations they represent)A 59 434 :M -.22(the )A 78 434 :M -.163(same )A 108 434 :M -.109(set )A 127 434 :M (of )S 143 434 :M -.15(probability )A 200 434 :M (distributions.\) )S 273 434 :M .258 .026(For )J 296 434 :M -.081(example, )A 345 434 :M -.22(the )A 365 434 :M -.073(following )A 417 434 :M (two )S 441 434 :M -.164(DAGs )A 477 434 :M -.323(are)A 59 458 :M -.094(faithfully indistinguishable.)A 251 506 :M f0_12 sf 2.949 .295(Figure 1)J 59 554 :M f1_12 sf -.134(For each DAG )A f2_12 sf -.205(G)A f1_12 sf -.109(, there is a set of DAGs that are faithfully indistinguishable from it; we call)A 59 578 :M -.092(this the faithful indistinguishabilty class of )A f2_12 sf -.181(G)A f1_12 sf -.094(. The faithful indistinguishability class of \(i\) in)A 59 602 :M -.054(Figure )A 94 602 :M (1 )S 104 602 :M (consists )S 146 602 :M (of )S 160 602 :M -.22(the )A 178 602 :M -.164(DAGs )A 212 602 :M -.107(\(i\) )A 227 602 :M -.109(and )A 248 602 :M .23 .023(\(ii\). )J 271 602 :M -.083(This )A 297 602 :M -.164(faithful )A 336 602 :M -.133(indistinguishability )A 431 602 :M -.064(class )A 459 602 :M -.217(can )A 480 602 :M -.326(be)A 59 626 :M -.135(more compactly represented by )A 210 626 :M -.163(an )A 225 626 :M -.22(object )A 257 626 :M -.249(that )A 278 626 :M (we )S 296 626 :M -.33(call )A 316 626 :M -.065(\(following )A 370 626 :M -.328(Verma )A 405 626 :M -.109(and )A 426 626 :M -.13(Pearl )A 454 626 :M (1992\) )S 486 626 :M (a)S 59 650 :M f0_12 sf .249(pattern)A f1_12 sf .25 .025(. )J 106 650 :M -.128(Hence )A 140 650 :M -.326(a )A 149 650 :M -.188(pattern )A 185 650 :M -.063(represents )A 238 650 :M -.326(a )A 248 650 :M -.109(set )A 266 650 :M (of )S 281 650 :M -.164(DAGs )A 316 650 :M -.053(\(which )A 354 650 :M -.167(in )A 368 650 :M -.234(certain )A 404 650 :M -.188(special )A 441 650 :M -.062(cases )A 471 650 :M -.33(may)A 59 674 :M -.189(contain )A 97 674 :M -.083(only )A 122 674 :M -.109(one )A 143 674 :M -.038(member\). )A 193 674 :M -.663(A )A 205 674 :M -.188(pattern )A 241 674 :M (is )S 253 674 :M -.326(a )A 262 674 :M -.165(type )A 287 674 :M (of )S 302 674 :M -.064(graph )A 334 674 :M -.249(that )A 356 674 :M -.217(can )A 377 674 :M -.189(contain )A 416 674 :M -.083(both )A 442 674 :M -.182(undirected)A endp %%Page: 5 5 %%BeginPageSetup initializepage (peter; page: 5 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.064(edges and directed edges. )A 184 50 :M -.219(The )A 206 50 :M -.188(pattern )A 242 50 :M -.108(representing )A 304 50 :M -.22(the )A 322 50 :M -.164(faithful )A 360 50 :M -.133(indistinguishability )A 454 50 :M -.064(class )A 481 50 :M (of)S 59 74 :M (\(i\) in Figure 1 is shown in Figure 2.)S 251 98 :M f0_12 sf 2.949 .295(Figure 2)J 59 122 :M f1_12 sf -.121(We will not explain here the rules for )A 238 122 :M -.18(determining )A 298 122 :M -.092(whether )A 340 122 :M -.326(a )A 349 122 :M -.132(given )A 379 122 :M -.33(DAG )A 408 122 :M .306 .031(G )J 421 122 :M (is )S 433 122 :M -.167(in )A 446 122 :M -.22(the )A 464 122 :M -.109(set )A 481 122 :M (of)S 59 146 :M -.164(DAGs )A 93 146 :M -.117(represented )A 151 146 :M (by )S 167 146 :M -.326(a )A 176 146 :M -.039(pattern. )A 216 146 :M -.108(See )A 238 146 :M 1.182 .118(CPS, )J 269 146 :M -.109(and )A 291 146 :M -.046(Glymour )A 339 146 :M -.066(\(this )A 365 146 :M -.141(volume\) )A 409 146 :M (for )S 428 146 :M -.163(more )A 457 146 :M -.046(details.)A 59 170 :M -.085(However, notice that when an oriented edge )A 271 170 :M .486 .049(\(e.g )J 294 170 :M f2_12 sf 1.185(X)A f1_12 sf .485 .048( )J 307 170 :M .199 .02(-> )J 322 170 :M f2_12 sf .652(Y)A f1_12 sf .621 .062(\) )J 338 170 :M -.167(in )A 351 170 :M -.108(figure )A 383 170 :M (2 )S 393 170 :M -.091(appears )A 433 170 :M -.167(in )A 446 170 :M -.326(a )A 455 170 :M -.045(pattern,)A 59 194 :M -.165(then )A 84 194 :M -.22(the )A 103 194 :M -.163(edge )A 130 194 :M f2_12 sf 1.185(X)A f1_12 sf .485 .048( )J 144 194 :M .199 .02(-> )J 160 194 :M f2_12 sf .917(Y)A f1_12 sf .412 .041( )J 173 194 :M -.052(occurs )A 209 194 :M -.167(in )A 223 194 :M f2_12 sf (every)S f1_12 sf ( )S 254 194 :M -.064(graph )A 287 194 :M -.167(in )A 302 194 :M -.22(the )A 322 194 :M -.109(set )A 341 194 :M -.117(represented )A 401 194 :M (by )S 419 194 :M -.22(the )A 439 194 :M -.039(pattern. )A 481 194 :M (In)S 59 218 :M -.009(contrast, when an unoriented edge \(e.g. )A f2_12 sf (Z)S f1_12 sf ( - )S f2_12 sf (W)S f1_12 sf -.009(\) appears in a )A 345 218 :M -.039(pattern, )A 385 218 :M -.165(then )A 409 218 :M -.22(the )A 427 218 :M (two )S 449 218 :M -.163(variables)A 59 242 :M -.334(it )A 69 242 :M -.122(connects )A 114 242 :M -.215(are )A 132 242 :M -.247(adjacent )A 174 242 :M -.167(in )A 187 242 :M -.129(every )A 217 242 :M -.33(DAG )A 246 242 :M -.167(in )A 259 242 :M -.22(the )A 277 242 :M -.109(set )A 294 242 :M -.117(represented )A 352 242 :M (by )S 368 242 :M -.22(the )A 386 242 :M -.039(pattern, )A 426 242 :M -.111(but )A 446 242 :M -.165(they )A 471 242 :M -.33(may)A 59 266 :M .018 .002(have different orientations \(e.g. )J f2_12 sf (Z)S f1_12 sf ( -> )S f2_12 sf (W)S f1_12 sf ( in \(i\) and )S f2_12 sf (W)S f1_12 sf ( -> )S f2_12 sf (Z)S f1_12 sf ( in \(ii\)\).)S 59 290 :M -.131(Since )A 89 290 :M -.331(all )A 104 290 :M (of )S 118 290 :M -.22(the )A 136 290 :M -.14(members )A 183 290 :M (of )S 197 290 :M -.326(a )A 206 290 :M -.164(faithful )A 244 290 :M -.133(indistinguishability )A 339 290 :M -.064(class )A 367 290 :M -.107(represent )A 415 290 :M -.22(the )A 434 290 :M -.163(same )A 463 290 :M -.109(set )A 481 290 :M (of)S 59 314 :M -.15(probability )A 116 314 :M (distributions, )S 185 314 :M -.334(it )A 197 314 :M (is )S 212 314 :M -.111(not )A 234 314 :M -.041(possible )A 280 314 :M -.167(to )A 296 314 :M -.219(determine )A 349 314 :M -.065(which )A 385 314 :M -.219(member )A 430 314 :M (of )S 447 314 :M -.22(the )A 468 314 :M -.08(class)A 59 338 :M -.085(generated a given distribution in the set. For )A 271 338 :M -.249(that )A 292 338 :M .405 .04(reason, )J 331 338 :M -.22(the )A 349 338 :M -.111(output )A 383 338 :M (of )S 397 338 :M -.22(the )A 415 338 :M .271 .027(PC )J 434 338 :M -.184(algorithm )A 483 338 :M (is)S 59 362 :M -.096(not a single DAG, but a faithful indistinguishability class represented by a pattern, )A 450 362 :M -.142(although)A 59 386 :M -.092(in some special cases, the set of DAGs represented by a pattern contains a single DAG.)A 59 410 :M -.219(The )A 81 410 :M .271 .027(PC )J 100 410 :M -.184(algorithm )A 149 410 :M -.131(takes )A 177 410 :M (as )S 191 410 :M -.134(input )A 220 410 :M -.165(sample )A 258 410 :M (data, )S 286 410 :M -.109(and )A 308 410 :M -.166(optional )A 351 410 :M -.065(background )A 412 410 :M .175 .018(knowledge. )J 473 410 :M -.328(The)A 59 434 :M -.184(algorithm )A 109 434 :M -.163(relies )A 139 434 :M (on )S 156 434 :M -.066(tests )A 182 434 :M (of )S 197 434 :M -.181(conditional )A 254 434 :M -.074(independence, )A 327 434 :M .277 .028(so )J 343 434 :M -.167(in )A 357 434 :M -.246(practice )A 398 434 :M -.326(a )A 409 434 :M (user )S 435 434 :M -.082(also )A 460 434 :M (has )S 482 434 :M -.334(to)A 59 458 :M -.101(assume something about the class of distributions that the population distribution )A 444 458 :M -.165(lies )A 464 458 :M .512 .051(in. )J 481 458 :M (In)S 59 482 :M -.113(implementations of the algorithm, we have allowed the user to assume that the population is)A 59 506 :M -.219(either )A 90 506 :M -.219(linear )A 121 506 :M -.165(normal )A 159 506 :M (or )S 174 506 :M -.034(discrete. )A 219 506 :M -.122(Freedman )A 271 506 :M -.083(dislikes )A 312 506 :M -.22(the )A 331 506 :M -.066(assumption )A 390 506 :M (of )S 406 506 :M -.22(linearity )A 450 506 :M -.167(in )A 465 506 :M -.22(many)A 59 530 :M .43 .043(cases, )J 94 530 :M -.111(but )A 115 530 :M -.084(this )A 138 530 :M -.066(assumption )A 198 530 :M (is )S 212 530 :M -.111(not )A 233 530 :M -.031(essential, )A 283 530 :M (as )S 299 530 :M -.083(long )A 326 530 :M (as )S 342 530 :M -.082(some )A 373 530 :M -.13(reasonable )A 429 530 :M -.153(distributional)A 59 554 :M -.094(assumption can )A 136 554 :M -.163(be )A 151 554 :M -.247(made )A 180 554 :M -.065(which )A 213 554 :M -.219(enable )A 247 554 :M -.22(the )A 265 554 :M -.184(algorithm )A 314 554 :M -.167(to )A 327 554 :M -.247(make )A 356 554 :M -.111(judgments )A 409 554 :M -.132(about )A 439 554 :M -.199(conditional)A 59 578 :M -.074(independence. )A 133 578 :M -.328(Of )A 151 578 :M .405 .04(course, )J 192 578 :M -.22(the )A 212 578 :M -.111(distribution )A 272 578 :M -.22(may )A 298 578 :M -.219(either )A 331 578 :M -.163(be )A 349 578 :M -.231(completely )A 407 578 :M .742 .074(unknown, )J 463 578 :M (or )S 480 578 :M .333(so)A 59 602 :M -.138(complicated as to make judgments about conditional independence impossible in practice.)A 59 626 :M -.219(The )A 81 626 :M -.087(correctness )A 138 626 :M -.188(theorem )A 180 626 :M (for )S 198 626 :M -.22(the )A 216 626 :M .271 .027(PC )J 235 626 :M -.184(algorithm )A 284 626 :M -.109(states )A 314 626 :M -.249(that )A 335 626 :M -.041(assuming )A 384 626 :M -.107(\(i\) )A 399 626 :M -.22(the )A 417 626 :M -.11(Causal )A 454 626 :M -.197(Markov)A 59 650 :M -.07(Condition, \(ii\) the )A 148 650 :M -.054(Faithfulness )A 210 650 :M (Condition, )S 265 650 :M -.109(and )A 286 650 :M -.198(\(iii\) )A 307 650 :M -.163(causal )A 340 650 :M -.118(sufficiency )A 396 650 :M .898 .09(\(i.e. )J 420 650 :M -.129(every )A 450 650 :M -.199(common)A 59 674 :M -.129(cause )A 93 674 :M (of )S 111 674 :M -.326(a )A 124 674 :M -.163(pair )A 150 674 :M (of )S 168 674 :M -.122(measured )A 221 674 :M -.145(variables )A 271 674 :M (is )S 287 674 :M -.165(itself )A 318 674 :M (measured\), )S 379 674 :M -.165(then )A 407 674 :M -.08(from )A 439 674 :M -.199(conditional)A endp %%Page: 6 6 %%BeginPageSetup initializepage (peter; page: 6 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.164(independence )A 128 50 :M -.146(relations )A 173 50 :M -.163(true )A 197 50 :M -.167(in )A 212 50 :M -.22(the )A 232 50 :M -.03(population, )A 292 50 :M -.22(the )A 312 50 :M .271 .027(PC )J 333 50 :M -.184(algorithm )A 384 50 :M -.048(outputs )A 425 50 :M -.326(a )A 436 50 :M -.188(pattern )A 474 50 :M -.331(that)A 59 74 :M -.094(represents the faithful indistinguishability class of the true causal DAG. For example, )A 465 74 :M -.165(given)A 59 98 :M -.326(a )A 68 98 :M -.111(distribution )A 127 98 :M -.181(generated )A 177 98 :M (by )S 194 98 :M -.22(the )A 213 98 :M -.064(graph )A 245 98 :M -.107(\(i\) )A 261 98 :M -.167(in )A 275 98 :M -.054(Figure )A 311 98 :M .833 .083(1, )J 326 98 :M -.22(the )A 345 98 :M -.111(output )A 380 98 :M (of )S 395 98 :M -.22(the )A 414 98 :M -.184(algorithm )A 464 98 :M (is )S 477 98 :M -.33(the)A 59 122 :M -.012(pattern shown in Figure 2.)A 59 146 :M f0_12 sf 4.784 .478(2. Assumptions)J 59 170 :M f1_12 sf -.157(According to Freedman:)A 77 218 :M -.197(Their )A 106 218 :M -.132(algorithms )A 160 218 :M -.053([those )A 193 218 :M (found )S 225 218 :M -.167(in )A 238 218 :M .472 .047(CPS] )J 268 218 :M -.163(have )A 294 218 :M -.082(some )A 323 218 :M -.256(technical )A 368 218 :M -.035(interest, )A 410 218 :M -.111(but )A 429 218 :M -.166(will )A 452 218 :M -.329(make)A 77 242 :M -.163(causal )A 111 242 :M -.129(inferences )A 164 242 :M -.083(only )A 190 242 :M (when )S 221 242 :M -.146(causation )A 270 242 :M (is )S 283 242 :M -.046(assumed )A 329 242 :M -.167(in )A 343 242 :M -.22(the )A 362 242 :M -.064(first )A 386 242 :M -.052(place. )A 419 242 :M -.165(To )A 437 242 :M -.163(be )A 453 242 :M -.218(more)A 77 266 :M -.258(explicit: )A 118 266 :M (If )S 130 266 :M (we )S 148 266 :M -.053(assume )A 187 266 :M -.249(that )A 208 266 :M -.22(the )A 226 266 :M .223 .022(arrows )J 263 266 :M -.167(in )A 276 266 :M -.326(a )A 285 266 :M -.165(path )A 310 266 :M -.188(diagram )A 353 266 :M -.107(represent )A 401 266 :M -.146(causation )A 450 266 :M -.195(rather)A 77 290 :M -.165(than )A 101 290 :M -.026(association, )A 161 290 :M -.109(and )A 182 290 :M (we )S 200 290 :M -.082(also )A 223 290 :M -.053(assume )A 262 290 :M -.249(that )A 283 290 :M -.22(the )A 301 290 :M -.165(path )A 325 290 :M -.188(diagram )A 368 290 :M -.217(can )A 389 290 :M -.163(be )A 405 290 :M -.22(estimated )A 454 290 :M -.107(from)A 77 314 :M -.023(data, then indeed SGS can infer causation from association. ... Even )A 405 314 :M 1.025 .103(so, )J 424 314 :M -.183(causality )A 469 314 :M (is)S 77 338 :M -.072(assumed into the picture at the beginning, not proved in at the end. \(Freedman, 65\))A 59 386 :M -.164(It )A 71 386 :M (is )S 84 386 :M -.111(not )A 104 386 :M -.261(clear )A 131 386 :M -.081(what )A 159 386 :M -.084(this )A 181 386 :M -.045(passage )A 223 386 :M .217 .022(means. )J 262 386 :M -.219(The )A 286 386 :M -.111(output )A 322 386 :M (of )S 338 386 :M -.22(the )A 358 386 :M .271 .027(PC )J 379 386 :M -.184(algorithm )A 430 386 :M (is )S 444 386 :M -.326(a )A 455 386 :M -.045(pattern,)A 59 410 :M -.128(typically not a path diagram \(or DAG\). We )A 265 410 :M (do )S 281 410 :M -.111(simply )A 317 410 :M -.053(assume )A 356 410 :M -.249(that )A 377 410 :M -.22(the )A 395 410 :M -.247(data )A 418 410 :M (is )S 430 410 :M -.181(generated )A 479 410 :M (by)S 59 434 :M f2_12 sf .077(some)A f1_12 sf ( )S 88 434 :M -.163(causal )A 121 434 :M .567 .057(process. )J 166 434 :M -.326(We )A 187 434 :M (do )S 204 434 :M -.111(not )A 224 434 :M -.111(simply )A 261 434 :M -.053(assume )A 301 434 :M -.249(that )A 323 434 :M -.22(the )A 342 434 :M -.111(output )A 377 434 :M (of )S 392 434 :M -.22(the )A 411 434 :M -.184(algorithm )A 461 434 :M -.131(\(given)A 59 458 :M -.135(correct judgments )A 147 458 :M -.132(about )A 177 458 :M -.133(population )A 231 458 :M -.181(conditional )A 287 458 :M -.164(independence )A 355 458 :M -.131(relations\) )A 403 458 :M -.063(represents )A 455 458 :M -.326(a )A 464 458 :M -.109(set )A 481 458 :M (of)S 59 482 :M .226 .023(DAGS, )J 101 482 :M -.109(one )A 124 482 :M (of )S 140 482 :M -.065(which )A 175 482 :M (is )S 189 482 :M -.326(a )A 200 482 :M -.186(correct )A 238 482 :M -.12(description )A 296 482 :M (of )S 312 482 :M -.249(that )A 335 482 :M -.163(causal )A 370 482 :M .567 .057(process. )J 416 482 :M -.326(We )A 438 482 :M f2_12 sf -.148(derive)A f1_12 sf ( )S 474 482 :M -.331(that)A 59 506 :M -.069(conclusion from the Causal Markov and Faithfulness conditions, and causal sufficiency. \(If)A 59 530 :M -.22(the )A 78 530 :M -.066(assumption )A 137 530 :M (of )S 152 530 :M -.163(causal )A 186 530 :M -.118(sufficiency )A 243 530 :M -.064(seems )A 277 530 :M -.081(unreasonably )A 346 530 :M -.167(in )A 361 530 :M -.326(a )A 372 530 :M -.197(particular )A 422 530 :M .236 .024(case, )J 452 530 :M -.22(the )A 472 530 :M .166(FCI)A 59 554 :M -.104(algorithm we proposed can be used in place of the PC algorithm.\) Moreover we believe that)A 59 578 :M -.119(these axioms are often )A 168 578 :M .202 .02(widely, )J 208 578 :M -.111(but )A 227 578 :M -.111(not )A 246 578 :M -.12(explicitly, )A 297 578 :M -.187(already )A 335 578 :M -.046(assumed )A 380 578 :M -.167(in )A 393 578 :M -.326(a )A 402 578 :M -.188(variety )A 438 578 :M (of )S 452 578 :M -.141(contexts)A 59 602 :M -.11(by practicing statisticians.)A 59 626 :M -.122(Freedman )A 110 626 :M -.147(complains )A 162 626 :M -.249(that )A 183 626 :M -.154("causality )A 233 626 :M (is )S 245 626 :M -.046(assumed )A 290 626 :M -.167(into )A 312 626 :M -.22(the )A 331 626 :M -.188(picture )A 368 626 :M -.33(at )A 381 626 :M -.22(the )A 400 626 :M .052 .005(beginning." )J 461 626 :M -.164(It )A 473 626 :M (is )S 486 626 :M (a)S 59 650 :M -.207(banality )A 100 650 :M -.249(that )A 121 650 :M -.045(drawing )A 164 650 :M -.163(causal )A 197 650 :M -.129(inferences )A 249 650 :M -.08(from )A 277 650 :M -.211(statistical )A 325 650 :M -.247(data )A 349 650 :M -.08(requires )A 392 650 :M -.166(making )A 432 650 :M -.033(assumptions)A 59 674 :M -.132(about )A 89 674 :M -.22(the )A 107 674 :M -.137(relationship )A 166 674 :M -.139(between )A 209 674 :M -.211(statistical )A 256 674 :M -.247(data )A 279 674 :M -.109(and )A 300 674 :M -.163(causal )A 334 674 :M (structure. )S 384 674 :M (Such )S 413 674 :M -.03(assumptions )A 477 674 :M -.323(are)A endp %%Page: 7 7 %%BeginPageSetup initializepage (peter; page: 7 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.105(even made by experimentalists \(who assume an instance of )A 341 50 :M -.22(the )A 359 50 :M -.11(Causal )A 395 50 :M -.164(Markov )A 436 50 :M (Condition.\))S 59 74 :M -.111(We fail to see the point in replacing a discussion of two precisely stated )A 399 74 :M .199 .02(axioms, )J 441 74 :M -.22(the )A 459 74 :M -.131(Causal)A 59 98 :M -.08(Markov and Causal Faithfulness Conditions, with complaints about something )A 434 98 :M .277 .028(so )J 449 98 :M -.13(vague )A 481 98 :M (as)S 59 122 :M -.102("causality is assumed into the picture at the beginning.")A 59 146 :M -.071(Instances )A 107 146 :M (of )S 121 146 :M -.22(the )A 139 146 :M -.11(Causal )A 175 146 :M -.164(Markov )A 217 146 :M -.112(Condition )A 269 146 :M -.215(are )A 288 146 :M -.046(assumed )A 334 146 :M -.167(in )A 348 146 :M -.326(a )A 358 146 :M -.081(wide )A 386 146 :M -.188(variety )A 423 146 :M (of )S 438 146 :M -.123(contexts )A 482 146 :M -.334(in)A 59 170 :M -.029(statistics. )A 107 170 :M -.131(Since )A 137 170 :M -.122(Freedman )A 188 170 :M (does )S 214 170 :M -.111(not )A 233 170 :M -.129(raise )A 259 170 :M -.132(objections )A 311 170 :M -.167(to )A 324 170 :M -.22(the )A 342 170 :M -.11(Causal )A 379 170 :M -.164(Markov )A 421 170 :M (Condition, )S 477 170 :M (we)S 59 194 :M -.05(will not discuss it further here.)A 59 218 :M -.219(The )A 83 218 :M -.054(Faithfulness )A 147 218 :M -.112(Condition )A 200 218 :M (is )S 214 218 :M -.15(essentially )A 269 218 :M -.163(an )A 286 218 :M -.066(assumption )A 346 218 :M -.249(that )A 369 218 :M -.181(conditional )A 427 218 :M -.179(independence)A 59 242 :M -.094(relations are generated because of the structure of the DAG \(i.e. for )A 380 242 :M -.331(all )A 395 242 :M -.193(parameterizations )A 481 242 :M (of)S 59 266 :M -.22(the )A 82 266 :M (DAG\), )S 124 266 :M -.162(rather )A 160 266 :M -.165(than )A 189 266 :M -.139(because )A 235 266 :M (of )S 254 266 :M -.22(the )A 277 266 :M -.163(parameters )A 337 266 :M .898 .09(\(i.e. )J 366 266 :M (for )S 389 266 :M .449 .045(some, )J 427 266 :M -.111(but )A 451 266 :M -.111(not )A 476 266 :M (all,)S 59 290 :M -.058(parameterizations of the DAG.\) In CPS \(Chapter 3\) we discuss a number of ways )A 449 290 :M -.167(in )A 462 290 :M -.081(which)A 59 314 :M -.22(the )A 79 314 :M -.054(Faithfulness )A 143 314 :M -.112(Condition )A 196 314 :M -.217(can )A 218 314 :M (fail. )S 243 314 :M -.33(One )A 268 314 :M (way )S 294 314 :M -.334(it )A 306 314 :M -.217(can )A 329 314 :M -.247(fail )A 351 314 :M (is )S 366 314 :M -.164(if )A 380 314 :M -.196(there )A 410 314 :M -.215(are )A 431 314 :M -.22(deterministic)A 59 338 :M -.093(relationships among measured variables. The path models in figure 3 )A 388 338 :M -.198(illustrate )A 432 338 :M -.14(another )A 471 338 :M (way)S 59 362 :M -.098(in which the Faithfulness Condition can fail \(where the error terms )A 377 362 :M -.163(have )A 403 362 :M -.163(been )A 429 362 :M -.237(omitted )A 468 362 :M -.107(from)A 59 386 :M -.034(the DAGs.\))A 251 410 :M f0_12 sf 2.949 .295(Figure 3)J 203 433 :M f2_12 sf .175 .017( X)J f1_12 sf .267 .027( = )J f4_12 sf .254(e)A f2_10 sf 0 2 rm (X)S 0 -2 rm 203 457 :M f2_12 sf .462(Y)A f1_12 sf .417 .042( = a )J f3_12 sf .456A f1_12 sf .189 .019( )J f2_12 sf .507(X)A f1_12 sf .384 .038( + )J f4_12 sf .365(e)A f2_10 sf 0 2 rm (Y)S 0 -2 rm 167 481 :M f2_12 sf .15 .015( Z)J f1_12 sf .241 .024( = b )J f3_12 sf .255A f1_12 sf .106 .011( )J f2_12 sf .259(Y)A f1_12 sf .233 .023( + c )J f3_12 sf .255A f1_12 sf .106 .011( )J f2_12 sf .284(X)A f1_12 sf .215 .022( + )J f4_12 sf .204(e)A f2_10 sf 0 2 rm (Z)S 0 -2 rm 59 506 :M f1_12 sf -.125(Suppose that the data were generated by a linear causal )A 321 506 :M (process )S 361 506 :M -.108(described )A 410 506 :M (by )S 426 506 :M -.33(DAG )A 455 506 :M .486 .049(\(i\), )J 474 506 :M -.163(and)A 59 530 :M -.22(the )A 78 530 :M -.061(error )A 106 530 :M -.131(terms )A 137 530 :M -.215(are )A 156 530 :M -.15(independent )A 218 530 :M -.165(normally )A 265 530 :M -.12(distributed )A 320 530 :M -.031(variables. )A 371 530 :M -.083(This )A 397 530 :M (does )S 424 530 :M -.111(not )A 444 530 :M -.276(entail )A 474 530 :M -.163(any)A 59 554 :M -.181(conditional )A 118 554 :M -.164(independence )A 189 554 :M -.146(relations )A 236 554 :M -.132(among )A 275 554 :M -.22(the )A 296 554 :M -.145(variables )A 346 554 :M (for )S 368 554 :M -.331(all )A 387 554 :M -.109(values )A 425 554 :M (of )S 443 554 :M -.22(the )A 465 554 :M -.263(linear)A 59 577 :M .007 .001(coefficients. However, if c = )J f3_12 sf (- )S 210 577 :M f1_12 sf -.326(a )A 219 577 :M f3_12 sf .285A f1_12 sf .13 .013( )J 230 577 :M .833 .083(b, )J 244 577 :M -.165(then )A 268 577 :M f2_12 sf 1.185(X)A f1_12 sf .485 .048( )J 281 577 :M -.109(and )A 302 577 :M f2_12 sf .917(Y)A f1_12 sf .412 .041( )J 314 577 :M -.215(are )A 332 577 :M -.054(independent. )A 397 577 :M (If )S 409 577 :M -.22(the )A 427 577 :M .271 .027(PC )J 446 577 :M -.207(algorithm)A 59 602 :M -.077(were )A 86 602 :M -.189(applied )A 124 602 :M -.167(to )A 137 602 :M -.084(this )A 159 602 :M (data, )S 187 602 :M -.334(it )A 198 602 :M (would )S 233 602 :M -.179(incorrectly )A 288 602 :M -.092(produce )A 331 602 :M -.326(a )A 341 602 :M -.188(pattern )A 378 602 :M .229 .023(whose )J 414 602 :M -.083(only )A 440 602 :M -.219(member )A 483 602 :M (is)S 59 626 :M -.094(model \(ii\). The distribution )A 191 626 :M (is )S 203 626 :M -.111(not )A 222 626 :M -.164(faithful )A 260 626 :M -.167(to )A 273 626 :M -.33(DAG )A 302 626 :M -.107(\(i\) )A 317 626 :M -.065(which )A 350 626 :M -.181(generated )A 399 626 :M .255 .026(it, )J 413 626 :M -.111(but )A 432 626 :M (is )S 444 626 :M -.164(faithful )A 482 626 :M -.334(to)A 59 650 :M -.33(DAG )A 89 650 :M -.164(\(ii\) )A 108 650 :M -.065(which )A 142 650 :M -.111(did )A 162 650 :M .476 .048(not. )J 186 650 :M -.083(This )A 213 650 :M (is )S 227 650 :M -.111(not )A 248 650 :M -.326(a )A 259 650 :M -.185(violation )A 306 650 :M (of )S 322 650 :M -.22(the )A 342 650 :M -.188(theorem )A 386 650 :M (we )S 406 650 :M -.053(proved )A 445 650 :M -.132(about )A 477 650 :M -.33(the)A 59 674 :M -.087(correctness )A 117 674 :M (of )S 132 674 :M -.22(the )A 151 674 :M .271 .027(PC )J 172 674 :M -.066(algorithm, )A 227 674 :M -.139(because )A 270 674 :M -.22(the )A 290 674 :M -.188(theorem )A 334 674 :M (assumes )S 380 674 :M -.249(that )A 403 674 :M -.22(the )A 423 674 :M -.111(distribution )A 483 674 :M (is)S endp %%Page: 8 8 %%BeginPageSetup initializepage (peter; page: 8 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.164(faithful )A 97 50 :M -.167(to )A 110 50 :M -.22(the )A 128 50 :M -.33(DAG )A 157 50 :M (of )S 171 50 :M -.22(the )A 189 50 :M -.163(causal )A 222 50 :M -.108(structure )A 267 50 :M -.249(that )A 288 50 :M -.181(generated )A 337 50 :M -.22(the )A 355 50 :M -.247(data )A 378 50 :M -.246(\(DAG )A 411 50 :M -.078(\(i\)\) )A 430 50 :M -.065(which )A 463 50 :M (is )S 476 50 :M -.167(not)A 59 74 :M -.076(true in this case. The examples that Freedman constructs in his section 11.3 adds nothing to)A 59 98 :M (our )S 80 98 :M (discussion )S 135 98 :M -.167(in )A 149 98 :M .503 .05(CPS )J 176 98 :M (of )S 191 98 :M -.079(indistinguishability, )A 290 98 :M -.109(and )A 312 98 :M -.22(the )A 331 98 :M -.164(examples )A 380 98 :M -.167(in )A 395 98 :M .714 .071(11.2 )J 423 98 :M -.109(and )A 446 98 :M .714 .071(12.3 )J 474 98 :M -.163(add)A 59 122 :M -.013(nothing to our discussion in CPS of faithfulness.)A 59 146 :M .571 .057(However, )J 112 146 :M -.22(the )A 131 146 :M -.245(mere )A 159 146 :M -.182(existence )A 207 146 :M (of )S 222 146 :M -.062(cases )A 252 146 :M -.062(where )A 286 146 :M -.22(the )A 306 146 :M -.054(Faithfulness )A 370 146 :M -.112(Condition )A 423 146 :M -.131(fails )A 449 146 :M (is )S 463 146 :M (of )S 479 146 :M (no)S 59 170 :M -.164(interest )A 97 170 :M -.167(in )A 110 170 :M (itself. )S 141 170 :M -.165(To )A 158 170 :M (draw )S 186 170 :M -.163(an )A 202 170 :M (analogy, )S 248 170 :M -.199(estimation )A 301 170 :M -.132(algorithms )A 356 170 :M -.217(can )A 377 170 :M -.247(fail )A 397 170 :M -.167(in )A 411 170 :M -.22(the )A 430 170 :M -.196(large )A 458 170 :M -.197(sample)A 59 194 :M -.108(limit on sets of measure 0; this is not an objection to )A 308 194 :M -.22(the )A 326 194 :M -.199(estimation )A 378 194 :M .188 .019(methods. )J 426 194 :M -.066(Similarly, )A 477 194 :M -.33(the)A 59 218 :M -.129(relevant question here is not the existence of data )A 293 218 :M (sets )S 315 218 :M (on )S 331 218 :M -.065(which )A 364 218 :M -.22(the )A 382 218 :M -.054(Faithfulness )A 444 218 :M -.126(Condition)A 59 242 :M -.101(will fail, but how likely it is that )A 214 242 :M -.334(it )A 224 242 :M -.166(will )A 246 242 :M (fail. )S 269 242 :M -.219(The )A 291 242 :M -.164(examples )A 339 242 :M -.249(that )A 360 242 :M -.122(Freedman )A 411 242 :M -.065(gives )A 440 242 :M -.167(in )A 453 242 :M -.093(sections)A 59 266 :M .455 .045(11.2, 12.3 don't even address this issue.)J 59 290 :M -.083(In the linear case, for a given )A 200 290 :M -.205(directed )A 241 290 :M -.33(DAG )A 270 290 :M 1.114 .111(G, )J 287 290 :M -.164(if )A 298 290 :M (we )S 316 290 :M -.245(parameterize )A 379 290 :M -.22(the )A 397 290 :M -.129(space )A 427 290 :M (of )S 441 290 :M -.11(models )A 479 290 :M (by)S 59 314 :M -.22(the )A 77 314 :M -.219(linear )A 107 314 :M -.163(coefficients )A 165 314 :M -.109(and )A 186 314 :M -.22(the )A 204 314 :M -.144(variances )A 252 314 :M (of )S 266 314 :M -.22(the )A 284 314 :M -.035(exogenous )A 339 314 :M -.031(variables, )A 389 314 :M -.22(the )A 407 314 :M -.15(probability )A 462 314 :M (of )S 477 314 :M -.33(the)A 59 338 :M -.054(Faithfulness )A 121 338 :M -.112(Condition )A 172 338 :M -.189(failing )A 206 338 :M -.167(in )A 219 338 :M -.22(the )A 238 338 :M -.133(population )A 293 338 :M (is )S 306 338 :M (of )S 321 338 :M -.122(Lebesgue )A 371 338 :M -.139(measure )A 415 338 :M .833 .083(0. )J 430 338 :M -.083(This )A 456 338 :M (has )S 477 338 :M -.33(the)A 59 362 :M -.087(consequence that any Bayesian who, conditional on )A 307 362 :M -.219(belief )A 337 362 :M -.167(in )A 350 362 :M -.326(a )A 359 362 :M -.163(causal )A 392 362 :M -.108(structure )A 437 362 :M -.129(represented)A 59 386 :M (by )S 76 386 :M f2_12 sf .79(G)A f1_12 sf .497 .05(, )J 94 386 :M (has )S 115 386 :M -.326(a )A 125 386 :M -.111(distribution )A 185 386 :M -.08(over )A 212 386 :M -.22(the )A 232 386 :M -.219(linear )A 264 386 :M -.163(parameters )A 321 386 :M -.249(that )A 344 386 :M (is )S 358 386 :M -.132(absolutely )A 412 386 :M -.066(continuous )A 470 386 :M -.11(with)A 59 410 :M -.122(Lebesgue )A 109 410 :M (measure, )S 157 410 :M .199 .02(assigns )J 197 410 :M -.139(measure )A 241 410 :M (0 )S 252 410 :M -.167(to )A 266 410 :M -.326(a )A 276 410 :M -.185(violation )A 322 410 :M (of )S 338 410 :M -.22(the )A 358 410 :M -.054(Faithfulness )A 422 410 :M (Condition. )S 479 410 :M -.656(Of)A 59 434 :M -.052(course )A 94 434 :M (we )S 112 434 :M -.164(cannot )A 147 434 :M -.107(prescribe )A 194 434 :M -.081(what )A 221 434 :M (priors )S 253 434 :M -.326(a )A 262 434 :M -.123(Bayesian )A 310 434 :M -.067(ought )A 342 434 :M -.167(to )A 356 434 :M .232 .023(have, )J 387 434 :M -.111(but )A 407 434 :M (we )S 426 434 :M -.134(think )A 455 434 :M -.249(that )A 477 434 :M -.33(the)A 59 458 :M -.102(kind of prior that we have described is implicitly held by many people in many cases.)A 59 482 :M -.064(James )A 92 482 :M (Robins )S 130 482 :M -.071(\(personal )A 178 482 :M -.189(communication\) )A 258 482 :M (has )S 278 482 :M -.108(raised )A 310 482 :M -.036(questions )A 359 482 :M (of )S 374 482 :M -.326(a )A 384 482 :M -.163(more )A 413 482 :M -.15(interesting )A 467 482 :M .085(type.)A 59 506 :M -.326(We )A 79 506 :M -.166(will )A 101 506 :M -.081(consider )A 145 506 :M -.161(here )A 169 506 :M -.109(one )A 190 506 :M -.166(simple )A 225 506 :M -.183(variation )A 270 506 :M (of )S 284 506 :M -.22(the )A 302 506 :M -.083(kind )A 327 506 :M (of )S 341 506 :M -.083(question )A 385 506 :M -.163(he )A 400 506 :M .893 .089(asks. )J 429 506 :M .197 .02(Suppose )J 474 506 :M -.331(that)A 59 529 :M -.117(from a sample the population is )A 211 529 :M -.11(judged )A 247 529 :M -.167(to )A 260 529 :M -.163(be )A 275 529 :M -.164(faithful )A 313 529 :M -.167(to )A 326 529 :M f2_12 sf .175(G)A f1_10 sf 0 2 rm .101(2)A 0 -2 rm f1_12 sf .061 .006( )J 344 529 :M -.111(but )A 363 529 :M -.111(not )A 382 529 :M f2_12 sf .589(G)A f1_10 sf 0 2 rm .34(1)A 0 -2 rm f1_12 sf .371 .037(. )J 404 529 :M -.33(One )A 427 529 :M (would )S 461 529 :M -.262(expect)A 59 553 :M -.121(that the probability of )A f2_12 sf -.235(G)A f1_10 sf 0 2 rm -.136(2)A 0 -2 rm f1_12 sf -.133( given the data )A 249 553 :M (would )S 283 553 :M -.163(be )A 298 553 :M -.047(boosted )A 339 553 :M -.247(relative )A 377 553 :M -.167(to )A 390 553 :M -.22(the )A 408 553 :M -.15(probability )A 463 553 :M (of )S 477 553 :M f2_12 sf .214(G)A f1_10 sf 0 2 rm (1)S 0 -2 rm 59 577 :M f1_12 sf -.132(given )A 92 577 :M -.22(the )A 113 577 :M (data, )S 143 577 :M -.139(because )A 187 577 :M -.131(while )A 220 577 :M f2_12 sf -.45(all)A f1_12 sf ( )S 238 577 :M -.193(parameterizations )A 327 577 :M (of )S 345 577 :M f2_12 sf .175(G)A f1_10 sf 0 2 rm .101(2)A 0 -2 rm f1_12 sf .061 .006( )J 367 577 :M -.215(are )A 389 577 :M -.231(compatible )A 448 577 :M -.083(with )A 477 577 :M -.33(the)A 59 602 :M -.135(conditional independence relations judged to hold )A 296 602 :M -.167(in )A 309 602 :M -.22(the )A 327 602 :M -.03(population, )A 385 602 :M -.083(only )A 410 602 :M -.326(a )A 419 602 :M -.231(relatively )A 466 602 :M -.249(small)A 59 625 :M -.109(set )A 76 625 :M (of )S 90 625 :M -.193(parameterizations )A 176 625 :M (of )S 190 625 :M f2_12 sf .175(G)A f1_10 sf 0 2 rm .101(1)A 0 -2 rm f1_12 sf .061 .006( )J 208 625 :M -.215(are )A 226 625 :M -.119(compatible. )A 285 625 :M -.113(But )A 306 625 :M .259 .026(how )J 331 625 :M -.196(large )A 358 625 :M (is )S 370 625 :M -.084(this )A 391 625 :M (boost )S 422 625 :M -.167(in )A 436 625 :M -.06(probability,)A 59 649 :M -.146(and might it not )A 137 649 :M -.163(be )A 152 649 :M -.118(overwhelmed )A 220 649 :M (by )S 236 649 :M (priors )S 268 649 :M -.081(favoring )A 312 649 :M f2_12 sf .175(G)A f1_10 sf 0 2 rm .101(1)A 0 -2 rm f1_12 sf .061 .006( )J 330 649 :M -.08(over )A 355 649 :M f2_12 sf (G)S f1_10 sf 0 2 rm (2)S 0 -2 rm f1_12 sf (? )S 378 649 :M -.165(To )A 395 649 :M -.165(test )A 415 649 :M .443 .044(this, )J 440 649 :M (we )S 458 649 :M -.111(did )A 477 649 :M -.33(the)A 59 674 :M -.073(following )A 111 674 :M -.123(Bayesian )A 160 674 :M .182 .018(analysis. )J 208 674 :M -.326(We )A 230 674 :M -.181(generated )A 281 674 :M (2000 )S 311 674 :M -.165(sample )A 351 674 :M -.247(data )A 377 674 :M -.056(points )A 413 674 :M -.08(from )A 443 674 :M -.326(a )A 455 674 :M -.131(random)A endp %%Page: 9 9 %%BeginPageSetup initializepage (peter; page: 9 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.226(parameterization )A 140 50 :M (of )S 154 50 :M -.33(DAG )A 183 50 :M -.164(\(ii\) )A 201 50 :M -.167(in )A 214 50 :M -.054(Figure )A 249 50 :M .833 .083(3, )J 263 50 :M -.062(where )A 296 50 :M -.245(each )A 321 50 :M (of )S 335 50 :M -.22(the )A 353 50 :M -.145(variables )A 399 50 :M (is )S 411 50 :M (ternary. )S 453 50 :M -.219(The )A 476 50 :M .325(PC)A 59 74 :M -.184(algorithm )A 110 74 :M -.181(correctly )A 157 74 :M (found )S 191 74 :M -.249(that )A 214 74 :M -.33(DAG )A 245 74 :M -.164(\(ii\) )A 265 74 :M -.181(generated )A 316 74 :M -.22(the )A 336 74 :M (data. )S 365 74 :M -.326(We )A 388 74 :M -.04(assigned )A 436 74 :M -.197(equal )A 468 74 :M -.08(prior)A 59 98 :M -.152(probabilities )A 122 98 :M -.167(to )A 136 98 :M -.33(DAG )A 166 98 :M -.107(\(i\) )A 182 98 :M -.109(and )A 204 98 :M -.33(DAG )A 234 98 :M .23 .023(\(ii\), )J 257 98 :M -.109(and )A 279 98 :M (we )S 298 98 :M -.04(assigned )A 344 98 :M -.326(a )A 354 98 :M -.294(Dirichlet )A 399 98 :M -.077(distributions )A 463 98 :M -.167(to )A 477 98 :M -.33(the)A 59 122 :M -.163(parameters )A 116 122 :M (of )S 133 122 :M -.33(DAG )A 165 122 :M -.107(\(i\) )A 183 122 :M -.109(and )A 207 122 :M -.33(DAG )A 239 122 :M .23 .023(\(ii\). )J 264 122 :M -.162(\(The )A 293 122 :M -.111(distribution )A 354 122 :M (we )S 375 122 :M (used )S 404 122 :M .199 .02(assigns )J 446 122 :M -.22(the )A 467 122 :M -.218(same)A 59 146 :M -.15(probability )A 114 146 :M -.167(to )A 127 146 :M -.109(any )A 148 146 :M (two )S 170 146 :M -.165(faithfully )A 217 146 :M -.117(indistinguishable )A 301 146 :M -.164(DAGs )A 335 146 :M -.109(and )A 356 146 :M (is )S 369 146 :M -.108(described )A 419 146 :M -.167(in )A 433 146 :M -.033(Heckerman,)A 59 170 :M -.062(Geiger, and Chickering 1994\) We )A 224 170 :M -.165(then )A 248 170 :M -.263(calculated )A 298 170 :M -.22(the )A 316 170 :M -.197(ratio )A 341 170 :M (of )S 355 170 :M -.22(the )A 373 170 :M -.031(posteriors )A 424 170 :M (of )S 438 170 :M -.33(DAG )A 467 170 :M -.107(\(i\) )A 482 170 :M -.334(to)A 59 194 :M -.131(DAG \(ii\) given the data for 10 different )A 248 194 :M -.247(data )A 271 194 :M (sets )S 293 194 :M -.181(generated )A 342 194 :M -.08(from )A 369 194 :M -.109(random )A 409 194 :M -.205(parameterizations)A 59 218 :M (of )S 73 218 :M -.164(\(ii\) )A 91 218 :M -.062(where )A 124 218 :M -.245(each )A 149 218 :M -.205(variable )A 190 218 :M -.132(could )A 220 218 :M -.247(take )A 243 218 :M (on )S 259 218 :M -.196(three )A 286 218 :M -.144(different )A 330 218 :M .204 .02(values, )J 368 218 :M -.109(and )A 389 218 :M (10 )S 405 218 :M -.144(different )A 449 218 :M -.247(data )A 473 218 :M (sets)S 59 242 :M -.181(generated )A 108 242 :M -.08(from )A 135 242 :M -.109(random )A 176 242 :M -.193(parameterizations )A 263 242 :M (of )S 278 242 :M -.164(\(ii\) )A 297 242 :M -.062(where )A 331 242 :M -.245(each )A 357 242 :M -.205(variable )A 399 242 :M -.132(could )A 430 242 :M -.247(take )A 454 242 :M (on )S 471 242 :M (four)S 59 266 :M -.101(different values. \(We did the calculations using the K2 program lent to )A 395 266 :M .277 .028(us )J 410 266 :M (by )S 426 266 :M .38 .038(Cooper.\) )J 473 266 :M -.328(The)A 59 290 :M -.132(likelihood ratio of DAG \(ii\) to DAG \(i\) given the data for cases where each variable took )A 479 290 :M (on)S 59 314 :M -.136(three different values averaged )A 207 314 :M .254(10)A f1_10 sf 0 -3 rm .185(6.21)A 0 3 rm f1_12 sf .23 .023(, )J 245 314 :M -.109(and )A 266 314 :M (for )S 284 314 :M -.22(the )A 302 314 :M -.062(cases )A 331 314 :M -.062(where )A 364 314 :M -.245(each )A 389 314 :M -.205(variable )A 430 314 :M -.083(took )A 455 314 :M (on )S 471 314 :M (four)S 59 338 :M -.144(different )A 103 338 :M -.109(values )A 137 338 :M -.334(it )A 147 338 :M -.162(averaged )A 193 338 :M .254(10)A f1_10 sf 0 -3 rm .185(13.7)A 0 3 rm f1_12 sf .23 .023(. )J 232 338 :M .258 .026(For )J 254 338 :M -.22(the )A 273 338 :M -.161(case )A 298 338 :M -.062(where )A 332 338 :M -.22(the )A 351 338 :M -.163(true )A 374 338 :M -.199(model )A 408 338 :M (is )S 421 338 :M .23 .023(\(ii\), )J 444 338 :M -.084(this )A 466 338 :M -.082(gives)A 59 361 :M -.082(some )A 88 361 :M -.199(indication )A 138 361 :M (of )S 152 361 :M .259 .026(how )J 177 361 :M -.189(heavily )A 215 361 :M -.22(the )A 233 361 :M (priors )S 266 361 :M (would )S 301 361 :M -.163(have )A 328 361 :M -.167(to )A 342 361 :M -.062(favor )A 372 361 :M f2_12 sf .175(G)A f1_10 sf 0 2 rm .101(2)A 0 -2 rm f1_12 sf .061 .006( )J 391 361 :M -.106(before )A 426 361 :M (we )S 445 361 :M (would )S 480 361 :M -.326(be)A 59 386 :M -.147(justified )A 102 386 :M -.167(in )A 116 386 :M -.081(favoring )A 161 386 :M -.22(the )A 180 386 :M -.239(alternative )A 234 386 :M -.167(to )A 249 386 :M -.22(the )A 269 386 :M -.111(output )A 305 386 :M (of )S 321 386 :M -.22(the )A 341 386 :M .271 .027(PC )J 362 386 :M -.066(algorithm. )A 417 386 :M -.247(More )A 448 386 :M -.14(Bayesian)A 59 410 :M -.042(analyses of this kind, using different )A 236 410 :M .596 .06(graphs, )J 276 410 :M -.276(latent )A 305 410 :M -.031(variables, )A 355 410 :M -.109(and )A 376 410 :M -.144(different )A 420 410 :M (priors )S 452 410 :M -.08(over )A 477 410 :M -.33(the)A 59 434 :M -.058(parameters would be useful, and we plan to perform them.)A 59 458 :M f0_12 sf 3.161 .316(3. The Correctness Results)J 59 482 :M f1_12 sf -.109(The correctness theorem for the PC algorithm states )A 307 482 :M -.249(that )A 328 482 :M -.041(assuming )A 377 482 :M -.22(the )A 395 482 :M -.247(data )A 418 482 :M (is )S 430 482 :M -.181(generated )A 479 482 :M (by)S 59 506 :M -.09(some causal DAG, the Causal Markov and Faithfulness )A 325 506 :M .155 .016(Conditions, )J 385 506 :M -.109(and )A 406 506 :M -.163(causal )A 439 506 :M -.13(sufficiency)A 59 530 :M -.034(\(i.e. every common cause of )A 198 530 :M -.326(a )A 207 530 :M -.163(pair )A 229 530 :M (of )S 243 530 :M -.122(measured )A 292 530 :M -.145(variables )A 338 530 :M (is )S 350 530 :M -.165(itself )A 377 530 :M (measured\), )S 434 530 :M -.165(then )A 458 530 :M -.22(the )A 476 530 :M .325(PC)A 59 554 :M -.117(algorithm outputs )A 146 554 :M -.326(a )A 155 554 :M -.188(pattern )A 191 554 :M -.249(that )A 212 554 :M -.063(represents )A 264 554 :M -.22(the )A 282 554 :M -.164(faithful )A 320 554 :M -.133(indistinguishability )A 414 554 :M -.064(class )A 441 554 :M (of )S 455 554 :M -.22(the )A 473 554 :M -.218(true)A 59 578 :M -.163(causal )A 93 578 :M -.33(DAG )A 123 578 :M (as )S 138 578 :M -.083(long )A 164 578 :M (as )S 179 578 :M -.112(its )A 196 578 :M -.132(judgements )A 256 578 :M -.132(about )A 288 578 :M -.181(conditional )A 346 578 :M -.164(independence )A 416 578 :M -.146(relations )A 462 578 :M -.167(in )A 477 578 :M -.33(the)A 59 602 :M -.133(population )A 116 602 :M -.215(are )A 137 602 :M -.037(correct. )A 180 602 :M -.166(Although )A 231 602 :M -.22(the )A 252 602 :M -.188(theorem )A 297 602 :M .264 .026(was )J 323 602 :M -.165(stated )A 357 602 :M -.064(under )A 391 602 :M -.22(the )A 412 602 :M -.066(assumption )A 474 602 :M -.331(that)A 59 626 :M -.109(population conditional independence facts were known it is easy to )A 378 626 :M .479 .048(show )J 408 626 :M -.249(that )A 429 626 :M -.22(the )A 447 626 :M -.111(output )A 481 626 :M (of)S 59 650 :M -.122(the PC algorithm is correct )A 189 650 :M -.083(with )A 214 650 :M -.15(probability )A 269 650 :M (1 )S 279 650 :M -.167(in )A 292 650 :M -.22(the )A 310 650 :M -.196(large )A 337 650 :M -.165(sample )A 374 650 :M -.112(limit, )A 403 650 :M -.164(if )A 414 650 :M -.141(instead )A 451 650 :M (of )S 465 650 :M -.165(being)A 59 674 :M -.132(given )A 89 674 :M -.133(population )A 143 674 :M -.181(conditional )A 199 674 :M -.164(independence )A 267 674 :M -.031(relations, )A 315 674 :M -.109(one )A 336 674 :M (is )S 348 674 :M -.132(given )A 379 674 :M -.326(a )A 389 674 :M -.064(class )A 417 674 :M (of )S 432 674 :M -.083(distributions)A endp %%Page: 10 10 %%BeginPageSetup initializepage (peter; page: 10 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.249(that )A 83 50 :M -.22(the )A 104 50 :M -.111(distribution )A 165 50 :M -.08(over )A 193 50 :M -.22(the )A 214 50 :M -.122(measured )A 266 50 :M -.145(variables )A 315 50 :M -.131(falls )A 342 50 :M .512 .051(in, )J 362 50 :M -.109(and )A 386 50 :M -.326(a )A 398 50 :M -.165(test )A 421 50 :M (of )S 439 50 :M -.199(conditional)A 59 74 :M -.164(independence )A 127 74 :M -.167(in )A 140 74 :M -.249(that )A 161 74 :M -.064(class )A 188 74 :M (of )S 202 74 :M -.077(distributions )A 265 74 :M -.065(which )A 298 74 :M (is )S 310 74 :M -.186(correct )A 346 74 :M -.083(with )A 371 74 :M -.15(probability )A 426 74 :M (1 )S 436 74 :M -.167(in )A 449 74 :M -.22(the )A 468 74 :M -.245(large)A 59 98 :M -.138(sample limit.)A 59 122 :M -.157(According to Freedman:)A 77 170 :M .765 .077(SGS )J 107 170 :M -.163(seem )A 138 170 :M -.167(to )A 154 170 :M -.331(claim )A 186 170 :M -.249(that )A 210 170 :M -.197(their )A 238 170 :M -.132(algorithms )A 295 170 :M -.166(will )A 320 170 :M -.082(find )A 346 170 :M -.331(all )A 364 170 :M (of )S 381 170 :M -.22(the )A 402 170 :M -.165(path )A 430 170 :M -.14(diagrams)A 77 194 :M -.101(compatible with a given covariance matrix. However, the )A 351 194 :M -.123(theorems )A 398 194 :M (suggest )S 438 194 :M -.249(that )A 459 194 :M -.33(the)A 77 218 :M -.01(algorithms will at best find one such DAG. \(Freedman, 49\)...)A 77 266 :M (In )S 93 266 :M -.211(statistical )A 142 266 :M -.055(terminology, )A 210 266 :M -.11(models )A 251 266 :M -.215(are )A 272 266 :M -.174("identifiable" )A 341 266 :M (when )S 374 266 :M -.165(they )A 401 266 :M -.247(make )A 433 266 :M -.163(different)A 77 290 :M -.12(predictions )A 134 290 :M -.132(about )A 165 290 :M .164 .016(observables. )J 230 290 :M .258 .026(For )J 252 290 :M -.081(example, )A 300 290 :M .2 .02(suppose )J 344 290 :M (you )S 367 290 :M -.163(have )A 395 290 :M (two )S 419 290 :M -.11(models )A 459 290 :M (for)S 77 314 :M -.03(your data. If, for all data sets)A 186 338 :M -.077(P\(data | model 1\) = P\(data | model 2\),)A 77 362 :M -.069(there is an obvious )A 170 362 :M -.108(problem-- )A 221 362 :M -.22(the )A 239 362 :M -.247(data )A 262 362 :M -.164(cannot )A 297 362 :M -.061(distinguish )A 353 362 :M -.139(between )A 396 362 :M -.22(the )A 414 362 :M .199 .02(models. )J 456 362 :M (If )S 468 362 :M (a)S 77 386 :M -.165(path )A 101 386 :M -.199(model )A 134 386 :M (is )S 146 386 :M -.109(complete, )A 196 386 :M (or )S 210 386 :M -.22(the )A 228 386 :M -.081(faithfulness )A 287 386 :M -.066(assumption )A 345 386 :M (is )S 358 386 :M -.111(not )A 378 386 :M .188 .019(imposed, )J 427 386 :M -.22(the )A 446 386 :M -.08(graph)A 77 410 :M -.139(underlying a covariance matrix is )A 237 410 :M -.111(not )A 256 410 :M -.229(identifiable; )A 315 410 :M 2.308 .231(... )J 331 410 :M .571 .057(However, )J 383 410 :M -.163(even )A 409 410 :M -.164(if )A 420 410 :M (we )S 438 410 :M -.064(assume)A 77 434 :M -.249(that )A 98 434 :M -.326(a )A 107 434 :M -.196(covariance )A 161 434 :M -.22(matrix )A 195 434 :M (is )S 208 434 :M -.164(faithful )A 247 434 :M -.167(to )A 261 434 :M -.326(a )A 271 434 :M -.064(graph )A 303 434 :M -.249(that )A 325 434 :M (is )S 338 434 :M -.111(not )A 358 434 :M -.109(complete, )A 409 434 :M -.196(there )A 437 434 :M -.22(may )A 462 434 :M -.326(be)A 77 458 :M -.139(several )A 115 458 :M (such )S 142 458 :M (graphs )S 179 458 :M .715 .072(\(SGS )J 211 458 :M .833 .083(p. )J 226 458 :M .719 .072(89\). )J 251 458 :M .258 .026(For )J 273 458 :M -.081(example, )A 321 458 :M -.22(the )A 340 458 :M -.073(following )A 391 458 :M -.196(three )A 419 458 :M (graphs )S 457 458 :M -.326(can)A 77 482 :M -.187(generate the same covariance matrix:)A 77 509 475 32 rC gS 27.819 1.778 scale 63.758 295.126 :T -63.758 -295.126 :T 6.758 298.126 :M f2_12 sf .104 .01(X Y Z)J gR 156 204 556 36 1717 523 @l 661 525 -28 2 1495 523 28 661 523 @a 156 204 556 36 3107 523 @l 2051 525 -28 2 2885 523 28 2051 523 @a gS 27.819 1.778 scale 196.651 295.126 :T -196.651 -295.126 :T 139.651 298.126 :M f2_12 sf .104 .01(X Y Z)J gR -24 24 556 36 4386 523 @l 4580 525 -28 2 5415 523 28 4580 523 @a 156 204 556 36 6804 523 @l 5748 525 -28 2 6582 523 28 5748 523 @a gS 27.819 1.778 scale 329.58 295.126 :T -329.58 -295.126 :T 272.58 298.126 :M f2_12 sf .104 .01(X Y Z)J gR -24 24 556 36 8083 523 @l 8278 525 -28 2 9112 523 28 8278 523 @a 156 204 556 36 10502 523 @l 9445 525 -28 2 10279 523 28 9445 523 @a gR gS 0 0 552 730 rC 77 586 :M f1_12 sf .668 .067(Thus, )J 110 586 :M .765 .077(SGS )J 138 586 :M (do )S 155 586 :M -.111(not )A 175 586 :M -.163(seem )A 205 586 :M -.167(to )A 220 586 :M -.163(have )A 248 586 :M -.144(succeeded )A 302 586 :M -.167(in )A 317 586 :M -.123(defining )A 362 586 :M -.326(a )A 373 586 :M -.064(class )A 402 586 :M (of )S 418 586 :M (graphs )S 456 586 :M -.163(and)A 77 610 :M -.062(covariance matrices for which identifiability holds... \(Freedman, 49\))A 59 658 :M -.083(This )A 86 658 :M -.045(passage )A 129 658 :M -.139(reveals )A 169 658 :M -.139(several )A 209 658 :M (confusions )S 268 658 :M -.249(that )A 292 658 :M -.122(Freedman )A 346 658 :M (has )S 369 658 :M -.132(about )A 402 658 :M -.22(the )A 423 658 :M -.111(output )A 460 658 :M (of )S 477 658 :M -.33(the)A 59 682 :M -.066(algorithm. )A 113 682 :M .626 .063(First, )J 144 682 :M (we )S 163 682 :M -.129(never )A 194 682 :M -.283(claimed )A 235 682 :M -.167(to )A 249 682 :M -.163(be )A 265 682 :M -.247(able )A 289 682 :M -.206(reliably )A 329 682 :M -.219(determine )A 380 682 :M -.326(a )A 390 682 :M -.11(unique )A 427 682 :M -.33(DAG )A 457 682 :M -.08(from )A 486 682 :M (a)S endp %%Page: 11 11 %%BeginPageSetup initializepage (peter; page: 11 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.196(covariance )A 113 50 :M -.046(matrix. )A 151 50 :M -.248(That )A 176 50 :M (is )S 188 50 :M .259 .026(why )J 213 50 :M -.164(if )A 224 50 :M -.22(the )A 242 50 :M -.247(data )A 265 50 :M (is )S 277 50 :M -.181(generated )A 326 50 :M (by )S 343 50 :M -.109(any )A 365 50 :M (of )S 380 50 :M -.22(the )A 399 50 :M -.196(three )A 427 50 :M -.163(causal )A 461 50 :M -.219(DAGs)A 59 74 :M -.112(Freedman refers to, the output of the algorithm is a pattern that represents )A f2_12 sf -.108(all three)A f1_12 sf -.177( DAGs.)A 59 98 :M -.034(Moreover, )A 113 98 :M -.245(each )A 138 98 :M -.33(DAG )A 167 98 :M -.167(in )A 180 98 :M -.22(the )A 198 98 :M -.109(set )A 215 98 :M -.117(represented )A 273 98 :M (by )S 289 98 :M -.22(the )A 307 98 :M -.188(pattern )A 343 98 :M (is )S 355 98 :M -.111(not )A 374 98 :M -.326(a )A 383 98 :M -.211(statistical )A 430 98 :M -.199(model )A 463 98 :M -.167(in )A 477 98 :M -.33(the)A 59 122 :M -.069(usual sense. That is, a DAG is not associated with one probability )A 374 122 :M -.025(distribution, )A 436 122 :M -.334(it )A 446 122 :M (is )S 458 122 :M -.165(instead)A 59 146 :M -.131(associated )A 114 146 :M -.083(with )A 143 146 :M -.326(a )A 156 146 :M -.109(set )A 177 146 :M (of )S 195 146 :M -.15(probability )A 254 146 :M -.077(distributions )A 321 146 :M -.053(\(which )A 362 146 :M -.064(under )A 397 146 :M -.22(the )A 419 146 :M -.066(assumption )A 481 146 :M (of)S 59 170 :M -.104(faithfulness all share )A 160 170 :M -.22(the )A 178 170 :M -.163(same )A 206 170 :M -.109(set )A 223 170 :M (of )S 237 170 :M -.181(conditional )A 293 170 :M -.164(independence )A 361 170 :M -.028(relations.\) )A 413 170 :M -.164(It )A 424 170 :M (is )S 436 170 :M -.083(only )A 461 170 :M -.195(after )A 486 170 :M (a)S 59 194 :M -.33(DAG )A 89 194 :M (is )S 102 194 :M -.227(parameterized )A 172 194 :M -.249(that )A 194 194 :M -.334(it )A 205 194 :M (is )S 218 194 :M -.131(associated )A 271 194 :M -.083(with )A 297 194 :M -.326(a )A 307 194 :M -.11(single )A 340 194 :M -.15(probability )A 396 194 :M -.025(distribution. )A 459 194 :M .274 .027(So )J 477 194 :M -.33(the)A 59 218 :M -.119(concept of identifiability as defined by Freedman does not even apply to )A 402 218 :M -.22(the )A 420 218 :M (graphs )S 456 218 :M -.249(that )A 477 218 :M -.323(are)A 59 242 :M -.099(represented by the output of the PC algorithm; P\(data | graph\) is not well )A 405 242 :M (defined. )S 448 242 :M -.326(We )A 468 242 :M -.103(were)A 59 266 :M (of )S 76 266 :M -.052(course )A 114 266 :M -.164(well )A 141 266 :M -.127(aware )A 176 266 :M (of )S 193 266 :M -.22(the )A 214 266 :M -.245(fact )A 238 266 :M -.08(\(and )A 266 266 :M -.197(repeatedly )A 321 266 :M -.148(emphasized\) )A 387 266 :M -.249(that )A 412 266 :M -.163(even )A 442 266 :M -.064(under )A 477 266 :M -.33(the)A 59 290 :M -.066(assumption )A 120 290 :M (of )S 137 290 :M (faithfulness, )S 203 290 :M -.249(that )A 227 290 :M -.196(there )A 257 290 :M -.132(exist )A 286 290 :M f2_12 sf -.303(parameterizations)A f1_12 sf ( )S 375 290 :M (of )S 392 290 :M -.22(the )A 413 290 :M -.196(three )A 443 290 :M (graphs )S 482 290 :M -.334(in)A 59 314 :M -.083(Freedman's example that represent the )A 244 314 :M -.163(same )A 272 314 :M -.196(covariance )A 326 314 :M -.046(matrix. )A 364 314 :M -.164(It )A 375 314 :M (is )S 387 314 :M -.326(a )A 396 314 :M -.166(simple )A 431 314 :M -.13(consequence)A 59 338 :M -.086(of a number of theorems described in Chapter 4 of )A 301 338 :M .503 .05(CPS )J 327 338 :M -.063(\(from )A 358 338 :M -.328(Verma )A 393 338 :M -.109(and )A 414 338 :M -.13(Pearl )A 442 338 :M .667 .067(1990, )J 474 338 :M -.163(and)A 59 362 :M -.056(Frydenberg 1990.\) It is for precisely this reason that the )A 327 362 :M -.111(output )A 361 362 :M (of )S 375 362 :M -.22(the )A 393 362 :M .271 .027(PC )J 412 362 :M -.184(algorithm )A 461 362 :M -.167(in )A 474 362 :M -.112(this)A 59 386 :M -.161(case )A 84 386 :M (is )S 97 386 :M -.111(not )A 117 386 :M -.326(a )A 127 386 :M -.11(single )A 160 386 :M (DAG, )S 194 386 :M -.111(but )A 214 386 :M -.326(a )A 224 386 :M -.188(pattern )A 261 386 :M -.065(which )A 296 386 :M -.063(represents )A 350 386 :M -.331(all )A 367 386 :M (3 )S 379 386 :M (of )S 395 386 :M -.22(the )A 415 386 :M .229 .023(DAGs. )J 455 386 :M -.221(And )A 481 386 :M (as)S 59 410 :M -.065(previously )A 114 410 :M -.065(explained, )A 168 410 :M (we )S 187 410 :M f2_12 sf -.144(have)A f1_12 sf ( )S 214 410 :M -.198(identified )A 263 410 :M (sets )S 286 410 :M (of )S 301 410 :M -.11(models )A 340 410 :M -.065(which )A 374 410 :M -.164(cannot )A 411 410 :M -.163(be )A 428 410 :M -.083(distinguished)A 59 434 :M -.08(from )A 90 434 :M -.245(each )A 120 434 :M -.131(other )A 153 434 :M -.132(given )A 188 434 :M -.084(just )A 214 434 :M -.326(a )A 228 434 :M -.15(probability )A 288 434 :M -.025(distribution, )A 355 434 :M -.041(assuming )A 409 434 :M -.11(Causal )A 450 434 :M (Markov,)S 59 458 :M .151 .015(Faithfulness, )J 125 458 :M -.109(and )A 146 458 :M -.163(causal )A 179 458 :M -.136(sufficiency; )A 238 458 :M -.084(this )A 259 458 :M (is )S 271 458 :M -.084(just )A 292 458 :M -.22(the )A 310 458 :M -.164(faithful )A 348 458 :M -.133(indistinguishability )A 443 458 :M -.064(class )A 471 458 :M (of )S 486 458 :M (a)S 59 482 :M (DAG.)S 59 506 :M (In )S 73 506 :M -.141(section )A 110 506 :M .714 .071(11.3 )J 136 506 :M -.122(Freedman )A 187 506 :M -.065(constructs )A 239 506 :M -.164(examples )A 287 506 :M (of )S 301 506 :M -.11(models )A 339 506 :M -.249(that )A 360 506 :M -.164(cannot )A 395 506 :M -.163(be )A 411 506 :M -.077(distinguished )A 479 506 :M (by)S 59 530 :M -.139(their correlation matrices. All of the examples of indistinguishability that )A 403 530 :M -.163(he )A 418 530 :M -.039(presents )A 461 530 :M -.167(in )A 474 530 :M -.112(this)A 59 554 :M -.141(section )A 96 554 :M -.215(are )A 114 554 :M -.166(simple )A 149 554 :M -.08(consequences )A 218 554 :M (of )S 232 554 :M -.22(the )A 250 554 :M -.133(indistinguishability )A 344 554 :M -.123(theorems )A 391 554 :M (we )S 409 554 :M -.197(state )A 434 554 :M -.167(in )A 447 554 :M -.187(chapter )A 485 554 :M (4)S 59 578 :M -.055(of CPS. Moreover, if data from any of the indistinguishable )A 346 578 :M -.11(models )A 384 578 :M -.077(were )A 411 578 :M -.132(given )A 441 578 :M -.167(to )A 454 578 :M -.22(the )A 472 578 :M .166(FCI)A 59 602 :M -.066(algorithm, )A 112 602 :M -.112(its )A 127 602 :M -.111(output )A 161 602 :M (would )S 195 602 :M -.163(be )A 210 602 :M -.326(a )A 219 602 :M -.109(set )A 237 602 :M (of )S 252 602 :M (graphs )S 289 602 :M -.249(that )A 311 602 :M -.183(contained )A 361 602 :M -.331(all )A 377 602 :M (of )S 392 602 :M -.22(the )A 411 602 :M -.124(indistinguishable)A 59 626 :M .057(models.)A 100 626 :M ( )S 59 650 :M -.12(The relevant questions about the output of the PC algorithm are:)A endp %%Page: 12 12 %%BeginPageSetup initializepage (peter; page: 12 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.073(1. Is the set of DAGs represented by the output of the PC algorithm )A 382 50 :M -.111(too )A 401 50 :M -.199(small )A 430 50 :M -.109(\(in )A 447 50 :M -.22(the )A 465 50 :M (sense)S 59 74 :M -.249(that )A 81 74 :M -.334(it )A 92 74 :M -.2(might )A 124 74 :M -.262(leave )A 153 74 :M -.111(out )A 173 74 :M -.22(the )A 192 74 :M -.163(true )A 215 74 :M -.262(DAG\)? )A 254 74 :M -.219(The )A 277 74 :M (answer )S 316 74 :M (is )S 329 74 :M .769 .077(no, )J 350 74 :M -.164(if )A 362 74 :M -.109(one )A 384 74 :M (assumes )S 429 74 :M .029(Faithfulness,)A 59 98 :M (Markov, )S 111 98 :M -.163(causal )A 151 98 :M -.025(sufficiency, )A 218 98 :M -.109(and )A 246 98 :M -.186(correct )A 290 98 :M -.211(statistical )A 345 98 :M -.073(decisions )A 401 98 :M -.132(about )A 439 98 :M -.199(conditional)A 59 122 :M -.08(independence.)A 59 146 :M -.066(2. Is the set of DAGs represented by the output of the )A 316 146 :M .271 .027(PC )J 335 146 :M -.184(algorithm )A 384 146 :M -.111(too )A 403 146 :M -.196(large )A 430 146 :M -.109(\(in )A 447 146 :M -.22(the )A 465 146 :M (sense)S 59 170 :M (that, )S 84 170 :M -.064(under )A 115 170 :M -.22(the )A 133 170 :M -.03(assumptions )A 196 170 :M (made, )S 229 170 :M -.082(some )A 258 170 :M -.33(DAG )A 287 170 :M -.117(represented )A 345 170 :M (by )S 361 170 :M -.22(the )A 379 170 :M -.111(output )A 413 170 :M -.188(pattern )A 449 170 :M (does )S 476 170 :M -.167(not)A 59 194 :M -.163(have )A 85 194 :M -.326(a )A 94 194 :M -.226(parameterization )A 175 194 :M -.249(that )A 196 194 :M -.165(faithfully )A 243 194 :M -.144(generates )A 291 194 :M -.22(the )A 309 194 :M -.163(true )A 331 194 :M -.025(distribution, )A 393 194 :M -.109(and )A 414 194 :M -.196(hence )A 445 194 :M -.132(could )A 476 194 :M -.167(not)A 59 218 :M -.163(be )A 76 218 :M -.18(correct?\) )A 123 218 :M -.265(Again )A 157 218 :M -.22(the )A 177 218 :M (answer )S 218 218 :M (is )S 233 218 :M .769 .077(no. )J 256 218 :M (\(In )S 277 218 :M .503 .05(CPS )J 306 218 :M (we )S 327 218 :M .215 .021(showed )J 371 218 :M -.249(that )A 395 218 :M -.245(each )A 423 218 :M (of )S 440 218 :M -.22(the )A 461 218 :M -.219(DAGs)A 59 242 :M -.145(represented by the output pattern entailed the conditional independence relations that hold )A 482 242 :M -.334(in)A 59 266 :M -.164(the true )A 98 266 :M -.025(distribution. )A 160 266 :M (Under )S 194 266 :M -.22(the )A 212 266 :M -.066(assumption )A 270 266 :M (of )S 284 266 :M -.163(causal )A 317 266 :M -.025(sufficiency, )A 377 266 :M -.109(and )A 398 266 :M -.22(the )A 416 266 :M -.182(existence )A 463 266 :M (of )S 477 266 :M -.33(the)A 59 290 :M -.132(right )A 85 290 :M -.181(conditional )A 141 290 :M -.094(density )A 179 290 :M .173 .017(functions, )J 231 290 :M -.084(this )A 252 290 :M -.189(entails )A 286 290 :M -.22(the )A 304 290 :M -.039(stronger )A 347 290 :M -.109(result )A 377 290 :M -.249(that )A 399 290 :M -.245(each )A 425 290 :M (of )S 440 290 :M -.22(the )A 459 290 :M (graphs)S 59 314 :M -.134(has a parameterization that faithfully generates the true distribution.\))A 382 314 :M ( )S 59 338 :M -.195(There )A 92 338 :M -.215(are )A 112 338 :M -.247(parallel )A 152 338 :M -.087(correctness )A 211 338 :M -.046(results )A 248 338 :M (for )S 268 338 :M -.22(the )A 288 338 :M -.131(other )A 318 338 :M -.132(algorithms )A 374 338 :M -.167(in )A 389 338 :M .503 .05(CPS )J 417 338 :M -.187(\(except )A 457 338 :M (for )S 477 338 :M -.33(the)A 59 362 :M -.066(algorithm described in Chapter 11, which is heuristic.\))A 59 386 :M -.031(In an artfully worded passage, )A 207 386 :M -.122(Freedman )A 258 386 :M -.067(hints )A 285 386 :M -.249(that )A 306 386 :M -.141(despite )A 343 386 :M (our )S 363 386 :M -.046(claims, )A 401 386 :M (we )S 419 386 :M -.266(ultimately )A 469 386 :M -.217(have)A 59 410 :M -.09(disavowed the possibility of discovering causal relations from )A 355 410 :M -.181(conditional )A 411 410 :M -.07(probabilities. )A 477 410 :M (He)S 59 434 :M (says:)S 77 482 :M .43 .043(SGS discuss )J 142 482 :M -.22(the )A 160 482 :M -.163(role )A 182 482 :M (of )S 196 482 :M -.03(assumptions )A 259 482 :M -.167(in )A 272 482 :M -.197(their )A 297 482 :M -.109(theory )A 331 482 :M -.139(several )A 368 482 :M -.199(times )A 397 482 :M .719 .072(\(pp. )J 421 482 :M .629 .063(53-69, )J 457 482 :M .5(pp.)A 77 506 :M .629 .063(75-81, )J 113 506 :M .769 .077(pp. )J 133 506 :M .629 .063(324-5, )J 170 506 :M .833 .083(p. )J 185 506 :M .671 .067(351\). )J 216 506 :M .571 .057(However, )J 269 506 :M -.22(the )A 288 506 :M -.204(clearest )A 328 506 :M -.22(statement )A 377 506 :M -.217(can )A 398 506 :M -.163(be )A 414 506 :M (found )S 447 506 :M (when)S 77 530 :M -.109(SGS are trying to discredit the evidence that smoking causes lung cancer:)A 95 578 :M -.138(effects )A 137 578 :M (**** )S 172 578 :M -.164(cannot )A 214 578 :M -.163(be )A 236 578 :M -.182(predicted )A 290 578 :M -.08(from )A 324 578 :M (**** )S 359 578 :M -.165(sample )A 403 578 :M -.199(conditional)A 95 602 :M (probabilities. [p. 302])S 77 650 :M -.092(Readers )A 119 650 :M -.22(may )A 143 650 :M -.094(consult )A 181 650 :M -.22(the )A 199 650 :M -.165(original )A 239 650 :M (for )S 257 650 :M -.04(context, )A 300 650 :M -.167(to )A 314 650 :M -.106(see )A 334 650 :M -.092(whether )A 377 650 :M -.22(the )A 396 650 :M -.237(omitted )A 436 650 :M -.33(material)A 77 674 :M -.138(affects )A 113 674 :M -.22(the )A 133 674 :M -.04(meaning. )A 183 674 :M -.219(The )A 207 674 :M -.182(advantage )A 260 674 :M (of )S 276 674 :M -.22(the )A 296 674 :M -.132(quote )A 328 674 :M (is )S 342 674 :M -.081(clarity. )A 381 674 :M (If )S 395 674 :M -.22(the )A 415 674 :M -.22(statement )A 465 674 :M (is)S endp %%Page: 13 13 %%BeginPageSetup initializepage (peter; page: 13 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 77 50 :M f1_12 sf -.113(generally applicable, then SGS-- like Yule and Pearl )A 327 50 :M -.106(before )A 361 50 :M -.163(them-- )A 396 50 :M -.163(have )A 422 50 :M -.04(disavowed)A 77 74 :M -.084(the ability to infer causation from association. \(Freedman, 24\))A 59 122 :M -.126(Here is the quote with the omitted )A 222 122 :M .451 .045(words )J 256 122 :M .19 .019(restored, )J 302 122 :M -.109(and )A 323 122 :M -.082(some )A 352 122 :M -.163(more )A 380 122 :M (of )S 394 122 :M -.22(the )A 412 122 :M -.11(beginning )A 463 122 :M (of )S 477 122 :M -.33(the)A 59 146 :M -.205(sentence:)A 77 194 :M -.041(...leading epidemiologists, such as Lillienfeld, seem simply not )A 381 194 :M -.167(to )A 394 194 :M -.163(have )A 420 194 :M -.036(understood)A 77 218 :M -.249(that )A 99 218 :M f2_12 sf .277 .028(if )J 111 218 :M -.22(the )A 130 218 :M -.374(relation )A 170 218 :M -.045(between )A 214 218 :M .594 .059(smoking )J 260 218 :M -.333(and )A 282 218 :M -.441(cancer )A 317 218 :M (is )S 330 218 :M (confounded )S 392 218 :M .561 .056(by )J 410 218 :M -.109(one )A 433 218 :M -.333(or )A 449 218 :M -.219(more)A 77 242 :M .217 .022(common )J 122 242 :M (causes)S f1_12 sf (, )S 161 242 :M -.22(the )A 180 242 :M -.138(effects )A 216 242 :M (of )S 231 242 :M -.1(abolishing )A 285 242 :M -.048(smoking )A 331 242 :M -.164(cannot )A 367 242 :M -.163(be )A 383 242 :M -.182(predicted )A 431 242 :M -.08(from )A 459 242 :M -.33(the)A 77 266 :M .073 .007("risk )J 104 266 :M .25 .025(ratios," )J 143 266 :M 1.56 .156(i.e., )J 168 266 :M -.08(from )A 196 266 :M -.165(sample )A 234 266 :M -.181(conditional )A 291 266 :M -.07(probabilities. )A 358 266 :M .359 .036(\(Spirtes, )J 404 266 :M .375 .038(Glymour, )J 456 266 :M -.163(and)A 77 290 :M -.029(Scheines 1993, 302, italics added\))A 59 338 :M -.16(The conversational implication of the )A 237 338 :M .451 .045(words )J 271 338 :M -.14(removed )A 316 338 :M (is )S 328 338 :M -.199(quite )A 355 338 :M -.273(clear; )A 384 338 :M -.164(if )A 395 338 :M -.22(the )A 413 338 :M -.206(relation )A 452 338 :M -.163(between)A 59 362 :M -.073(smoking and lung cancer is )A f2_12 sf -.075(not)A f1_12 sf -.078( confounded by one or more )A 344 362 :M -.166(common )A 389 362 :M .405 .04(causes, )J 428 362 :M -.22(the )A 446 362 :M -.138(effects )A 481 362 :M (of)S 59 386 :M -.123(abolishing smoking )A f2_12 sf -.139(can)A f1_12 sf -.122( be predicted from )A 261 386 :M -.165(sample )A 298 386 :M -.181(conditional )A 354 386 :M -.07(probabilities. )A 420 386 :M -.034(Moreover, )A 474 386 :M -.112(this)A 59 410 :M -.162(latter claim is a simple application of a theory developed at )A 337 410 :M -.166(length )A 370 410 :M -.167(in )A 383 410 :M -.141(Chapter )A 424 410 :M (7 )S 434 410 :M (of )S 448 410 :M .229 .023(CPS; )J 477 410 :M -.33(the)A 59 434 :M -.165(goal )A 83 434 :M (of )S 97 434 :M -.249(that )A 118 434 :M -.109(theory )A 153 434 :M .264 .026(was )J 177 434 :M -.167(to )A 191 434 :M -.092(specify )A 230 434 :M -.1(conditions )A 284 434 :M -.064(under )A 316 434 :M -.065(which )A 350 434 :M -.334(it )A 361 434 :M (is )S 374 434 :M -.041(possible )A 418 434 :M -.167(to )A 432 434 :M -.293(calculate )A 477 434 :M -.33(the)A 59 458 :M -.105(effects of interventions from conditional probabilities, )A 317 458 :M -.109(and )A 338 458 :M -.22(the )A 356 458 :M -.1(conditions )A 409 458 :M -.064(under )A 440 458 :M -.065(which )A 473 458 :M -.334(it )A 483 458 :M (is)S 59 482 :M .476 .048(not. )J 82 482 :M (In )S 96 482 :M -.22(the )A 114 482 :M -.189(context )A 152 482 :M (of )S 166 482 :M -.22(the )A 184 482 :M -.109(theory )A 218 482 :M -.146(developed )A 270 482 :M -.167(in )A 283 482 :M -.141(Chapter )A 324 482 :M .833 .083(7, )J 338 482 :M -.109(and )A 359 482 :M -.083(with )A 384 482 :M -.22(the )A 402 482 :M -.237(omitted )A 442 482 :M .451 .045(words )J 477 482 :M -.323(are)A 59 506 :M .19 .019(restored, )J 105 506 :M -.334(it )A 115 506 :M (is )S 127 506 :M -.261(clear )A 153 506 :M -.249(that )A 175 506 :M -.22(the )A 194 506 :M -.148(quotation )A 243 506 :M (is )S 256 506 :M -.163(an )A 272 506 :M f2_12 sf -.316(application)A f1_12 sf ( )S 328 506 :M (of )S 343 506 :M (our )S 364 506 :M .204 .02(theory, )J 403 506 :M -.111(not )A 423 506 :M -.326(a )A 433 506 :M f2_12 sf -.302(denial)A f1_12 sf ( )S 466 506 :M (of )S 481 506 :M .166(it.)A 59 530 :M -.093(\(Incidentally, )A 132 530 :M -.22(the )A 156 530 :M -.122(Freedman )A 213 530 :M -.148(quotation )A 267 530 :M -.139(reveals )A 310 530 :M -.14(another )A 355 530 :M -.179(fundamental )A 423 530 :M -.036(confusion )A 481 530 :M (of)S 59 554 :M -.099(Freedman's: the quotation concerns the possibility of making quantitative predictions )A 463 554 :M (of )S 477 554 :M -.33(the)A 59 578 :M -.138(effects )A 95 578 :M (of )S 110 578 :M -.163(causal )A 144 578 :M -.165(intervention )A 205 578 :M -.08(from )A 233 578 :M -.235(partial )A 267 578 :M -.072(knowledge )A 324 578 :M -.132(about )A 355 578 :M -.163(causal )A 389 578 :M -.108(structure )A 435 578 :M -.109(and )A 458 578 :M -.197(sample)A 59 602 :M -.15(probability )A 114 602 :M (distributions, )S 181 602 :M -.111(not )A 200 602 :M -.22(the )A 218 602 :M -.091(possibility )A 271 602 :M (of )S 285 602 :M -.108(inferring )A 331 602 :M -.121(features )A 373 602 :M (of )S 388 602 :M -.163(causal )A 422 602 :M -.108(structure )A 468 602 :M -.107(from)A 59 626 :M -.08(sample probability distributions.\))A 59 650 :M f0_12 sf 4.002 .4(4. Examples)J 59 674 :M f1_12 sf -.118(At the beginning of the discussion of empirical examples we said:)A endp %%Page: 14 14 %%BeginPageSetup initializepage (peter; page: 14 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 77 74 :M f1_12 sf -.132(We illustrate the algorithms for simulated and real data sets. With simulated )A 436 74 :M -.247(data )A 459 74 :M -.33(the)A 77 98 :M -.133(examples illustrate the properties of )A 248 98 :M -.22(the )A 266 98 :M -.132(algorithms )A 320 98 :M (on )S 336 98 :M -.093(samples )A 378 98 :M (of )S 392 98 :M -.219(realistic )A 432 98 :M .425 .042(sizes. )J 463 98 :M (In)S 77 122 :M -.098(the empirical cases we often do not know )A 276 122 :M -.092(whether )A 318 122 :M -.163(an )A 333 122 :M -.184(algorithm )A 382 122 :M -.039(produces )A 429 122 :M -.22(the )A 447 122 :M .068(truth.)A 77 146 :M -.151(But it is at the least )A 170 146 :M -.08(very )A 195 146 :M -.15(interesting )A 248 146 :M -.249(that )A 269 146 :M -.167(in )A 282 146 :M -.062(cases )A 311 146 :M -.167(in )A 324 146 :M -.065(which )A 357 146 :M -.101(investigators )A 421 146 :M -.163(have )A 447 146 :M -.165(given)A 77 170 :M -.132(some care to the treatment and explanation of their data, the algorithm reproduces )A 463 170 :M (or)S 77 194 :M -.163(nearly )A 110 194 :M -.063(reproduces )A 166 194 :M -.22(the )A 184 194 :M -.073(published )A 234 194 :M -.122(accounts )A 279 194 :M (of )S 293 194 :M -.163(causal )A 326 194 :M -.031(relations. )A 375 194 :M -.164(It )A 387 194 :M (is )S 400 194 :M -.082(also )A 424 194 :M -.165(interesting)A 77 218 :M -.249(that )A 103 218 :M -.167(in )A 121 218 :M -.062(cases )A 155 218 :M -.095(without )A 200 218 :M -.131(these )A 233 218 :M -.093(virtues )A 274 218 :M -.22(the )A 297 218 :M -.184(algorithm )A 351 218 :M .188 .019(suggests )J 401 218 :M -.199(quite )A 433 218 :M -.163(different)A 77 242 :M -.137(explanations )A 141 242 :M -.08(from )A 169 242 :M -.065(those )A 199 242 :M -.182(advocated )A 251 242 :M -.167(in )A 265 242 :M -.073(published )A 316 242 :M .381 .038(reports. )J 358 242 :M .359 .036(\(Spirtes, )J 404 242 :M .375 .038(Glymour, )J 456 242 :M -.163(and)A 77 266 :M .317 .032(Scheines 1993, 132-133.\))J 59 314 :M -.326(We )A 79 314 :M (do )S 95 314 :M -.111(not )A 114 314 :M -.134(think )A 142 314 :M -.249(that )A 163 314 :M .598 .06(Freedman's )J 223 314 :M -.09(substantive )A 280 314 :M -.165(criticisms )A 329 314 :M -.167(in )A 342 314 :M -.109(any )A 364 314 :M (way )S 389 314 :M -.197(contradict )A 440 314 :M -.084(this )A 462 314 :M -.131(claim.)A 59 338 :M -.065(We do not have room to discuss all of the criticisms, but we will discuss some of )A 446 338 :M -.22(the )A 464 338 :M -.247(major)A 59 362 :M .19 .019(ones here.)J 59 386 :M f0_12 sf 3.027 .303(4.1 The Timberlake-Williams example)J 59 410 :M f1_12 sf -.219(The )A 81 410 :M -.134(point )A 109 410 :M (of )S 123 410 :M (our )S 143 410 :M (discussion )S 197 410 :M (of )S 211 410 :M -.22(the )A 229 410 :M -.226(Timberlake-Williams )A 332 410 :M -.161(case )A 357 410 :M .264 .026(was )J 381 410 :M -.249(that )A 403 410 :M -.22(the )A 422 410 :M .255 .026(FCI )J 446 410 :M -.207(algorithm)A 59 434 :M -.081(produced )A 110 434 :M -.163(an )A 128 434 :M -.239(alternative )A 183 434 :M -.167(to )A 199 434 :M -.22(the )A 220 434 :M -.226(Timberlake-Williams )A 326 434 :M -.199(model )A 363 434 :M -.249(that )A 388 434 :M .264 .026(was )J 415 434 :M -.099(consistent )A 470 434 :M -.11(with)A 59 458 :M -.084(background knowledge, was testable and fit the data. We think that )A 380 458 :M -.084(this )A 401 458 :M .227 .023(sheds )J 432 458 :M -.148(considerable)A 59 482 :M -.067(doubt )A 90 482 :M (upon )S 118 482 :M -.22(the )A 136 482 :M -.226(Timberlake-Williams )A 239 482 :M (model. )S 276 482 :M (None )S 306 482 :M (of )S 320 482 :M .598 .06(Freedman's )J 380 482 :M -.091(remarks )A 422 482 :M -.215(are )A 440 482 :M -.205(relevant )A 482 482 :M -.334(to)A 59 506 :M (our )S 80 506 :M -.22(criticism )A 126 506 :M (of )S 142 506 :M -.22(the )A 162 506 :M -.226(Timberlake-Williams )A 267 506 :M (model. )S 306 506 :M -.122(Freedman )A 359 506 :M (does )S 387 506 :M -.111(not )A 408 506 :M -.134(think )A 438 506 :M -.109(any )A 461 506 :M (of )S 477 506 :M -.33(the)A 59 530 :M -.11(models )A 98 530 :M (discussed )S 149 530 :M -.132(\(including )A 202 530 :M -.22(the )A 221 530 :M -.109(one )A 243 530 :M -.119(constructed )A 302 530 :M -.08(from )A 330 530 :M -.22(the )A 349 530 :M -.111(output )A 384 530 :M (of )S 399 530 :M -.22(the )A 418 530 :M .255 .026(FCI )J 442 530 :M -.183(algorithm\))A 59 554 :M -.163(have )A 86 554 :M (good )S 115 554 :M -.205(evidence )A 161 554 :M (for )S 180 554 :M (them, )S 212 554 :M -.139(because )A 254 554 :M -.082(some )A 285 554 :M (of )S 301 554 :M -.22(the )A 321 554 :M -.03(assumptions )A 386 554 :M -.215(are )A 406 554 :M .555 .055(dubious, )J 454 554 :M -.109(and )A 477 554 :M -.33(the)A 59 578 :M -.165(sample )A 96 578 :M -.163(size )A 118 578 :M (is )S 130 578 :M (small. )S 163 578 :M -.326(We )A 183 578 :M (agree, )S 216 578 :M -.111(but )A 235 578 :M (we )S 254 578 :M -.129(never )A 285 578 :M -.247(made )A 315 578 :M -.109(any )A 337 578 :M -.331(claim )A 367 578 :M -.167(to )A 381 578 :M -.22(the )A 400 578 :M (contrary. )S 448 578 :M -.326(We )A 469 578 :M -.217(even)A 59 602 :M -.119(pointed out that we could )A 182 602 :M -.111(not )A 201 602 :M -.107(reproduce )A 252 602 :M -.22(the )A 270 602 :M -.179(correlation )A 324 602 :M -.22(matrix )A 358 602 :M -.122(reported )A 401 602 :M (by )S 417 602 :M -.23(Timberlake )A 474 602 :M -.163(and)A 59 626 :M -.249(Williams )A 106 626 :M -.08(from )A 134 626 :M -.22(the )A 153 626 :M (sources )S 194 626 :M -.165(they )A 219 626 :M -.064(cite. )A 244 626 :M -.219(Our )A 267 626 :M .259 .026(own )J 293 626 :M -.166(simulation )A 347 626 :M -.047(studies )A 385 626 :M -.22(indicated )A 433 626 :M -.249(that )A 456 626 :M -.22(the )A 476 626 :M .325(PC)A 59 650 :M -.184(algorithm )A 108 650 :M -.053(\(which )A 145 650 :M (is )S 157 650 :M -.109(considerably )A 221 650 :M -.141(simpler )A 260 650 :M -.165(than )A 284 650 :M -.22(the )A 302 650 :M .255 .026(FCI )J 325 650 :M -.165(algorithm\) )A 378 650 :M .264 .026(was )J 401 650 :M -.111(not )A 420 650 :M -.08(very )A 445 650 :M -.247(reliable )A 483 650 :M -.66(at)A 59 674 :M -.122(samples sizes considerably larger than that in the Timberlake-Williams studies.)A endp %%Page: 15 15 %%BeginPageSetup initializepage (peter; page: 15 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f0_12 sf 2.452 .245(4.2 The AFQT example)J 59 74 :M f1_12 sf -.101( We were given a variety of test scores \(which we will call the subtest scores\) and an AFQT)A 59 98 :M (score. The )S 113 98 :M -.332(AFQT )A 147 98 :M -.062(score )A 176 98 :M (is )S 188 98 :M -.263(calculated )A 238 98 :M -.08(from )A 265 98 :M -.082(some )A 294 98 :M (of )S 308 98 :M -.22(the )A 326 98 :M -.047(subtest )A 363 98 :M (scores )S 397 98 :M (we )S 415 98 :M -.077(were )A 442 98 :M .212 .021(given, )J 476 98 :M -.167(but)A 59 122 :M -.111(not )A 80 122 :M .4 .04(others. )J 119 122 :M -.219(The )A 143 122 :M -.134(point )A 173 122 :M (of )S 189 122 :M -.084(this )A 212 122 :M -.235(example )A 257 122 :M .264 .026(was )J 282 122 :M -.167(to )A 297 122 :M .479 .048(show )J 329 122 :M -.249(that )A 352 122 :M f2_12 sf (given )S 384 122 :M -.22(the )A 404 122 :M -.164(same )A 435 122 :M -.147(background)A 59 146 :M .167(knowledge)A f1_12 sf .16 .016(, )J 119 146 :M -.031(regression )A 172 146 :M -.131(techniques )A 226 146 :M -.132(could )A 256 146 :M -.111(not )A 275 146 :M -.082(find )A 298 146 :M -.22(the )A 316 146 :M -.099(components )A 377 146 :M (of )S 391 146 :M -.22(the )A 409 146 :M -.332(AFQT )A 443 146 :M .43 .043(score, )J 476 146 :M -.167(but)A 59 170 :M -.22(the )A 79 170 :M .271 .027(PC )J 101 170 :M -.109(and )A 125 170 :M .255 .026(FCI )J 151 170 :M -.132(algorithms )A 208 170 :M .248 .025(can. )J 235 170 :M -.122(Freedman )A 289 170 :M -.056(points )A 325 170 :M -.111(out )A 347 170 :M -.249(that )A 371 170 :M -.132(given )A 404 170 :M f2_12 sf -.146(more)A f1_12 sf ( )S 435 170 :M -.072(background)A 59 194 :M -.085(knowledge than was given to the )A 218 194 :M .271 .027(PC )J 237 194 :M -.109(and )A 258 194 :M .255 .026(FCI )J 281 194 :M -.029(algorithms, )A 339 194 :M -.031(regression )A 392 194 :M -.131(techniques )A 446 194 :M (would )S 480 194 :M -.326(be)A 59 218 :M -.149(able to pick out the )A 152 218 :M -.099(components )A 213 218 :M (of )S 227 218 :M -.22(the )A 245 218 :M -.332(AFQT )A 279 218 :M .43 .043(score. )J 312 218 :M (\(In )S 330 218 :M -.088(particular, )A 382 218 :M (his )S 400 218 :M -.031(regression )A 453 218 :M -.093(analysis)A 59 242 :M -.064(needs )A 90 242 :M (two )S 112 242 :M -.091(further )A 148 242 :M -.055(assumptions: )A 214 242 :M -.064(first )A 237 242 :M -.249(that )A 259 242 :M -.163(an )A 275 242 :M -.162(increase )A 318 242 :M -.167(in )A 332 242 :M -.326(a )A 342 242 :M -.147(component )A 399 242 :M -.062(score )A 429 242 :M -.107(increases )A 477 242 :M -.33(the)A 59 266 :M -.332(AFQT )A 93 266 :M .43 .043(score, )J 126 266 :M -.109(and )A 147 266 :M -.053(second )A 184 266 :M -.249(that )A 205 266 :M -.326(a )A 214 266 :M -.147(component )A 270 266 :M -.062(score )A 299 266 :M (is )S 311 266 :M -.111(not )A 331 266 :M -.111(highly )A 366 266 :M -.198(negatively )A 419 266 :M -.196(correlated )A 470 266 :M -.11(with)A 59 290 :M -.14(another )A 99 290 :M -.147(component )A 156 290 :M -.062(score )A 186 290 :M -.139(because )A 228 290 :M (of )S 243 290 :M -.326(a )A 253 290 :M -.166(common )A 299 290 :M .212 .021(cause.\) )J 338 290 :M -.084(Both )A 366 290 :M (of )S 382 290 :M -.131(these )A 412 290 :M -.03(assumptions )A 477 290 :M -.323(are)A 59 314 :M -.13(reasonable )A 114 314 :M -.167(in )A 128 314 :M -.084(this )A 150 314 :M .236 .024(case. )J 179 314 :M -.113(But )A 201 314 :M -.334(it )A 212 314 :M (does )S 239 314 :M -.111(not )A 259 314 :M -.247(take )A 283 314 :M -.079(away )A 313 314 :M -.08(from )A 342 314 :M -.22(the )A 362 314 :M -.245(fact )A 385 314 :M -.249(that )A 408 314 :M -.22(the )A 428 314 :M .271 .027(PC )J 449 314 :M -.109(and )A 472 314 :M .166(FCI)A 59 338 :M -.132(algorithms )A 116 338 :M -.163(derive )A 152 338 :M -.22(the )A 173 338 :M -.163(same )A 204 338 :M -.109(result )A 237 338 :M -.083(with )A 265 338 :M (less )S 290 338 :M -.054(information, )A 356 338 :M -.109(and )A 380 338 :M -.167(in )A 397 338 :M -.062(cases )A 430 338 :M -.062(where )A 467 338 :M -.163(these)A 59 362 :M -.065(background )A 120 362 :M -.03(assumptions )A 184 362 :M -.215(are )A 203 362 :M -.111(not )A 224 362 :M .277 .028(so )J 241 362 :M -.027(reasonable, )A 301 362 :M -.22(the )A 321 362 :M -.031(regression )A 376 362 :M -.183(technique )A 427 362 :M -.132(could )A 459 362 :M -.111(not )A 480 362 :M -.326(be)A 59 386 :M -.072(employed. Freedman )A 163 386 :M -.082(also )A 186 386 :M -.056(points )A 219 386 :M -.111(out )A 238 386 :M -.124(although )A 283 386 :M -.22(the )A 301 386 :M .271 .027(PC )J 320 386 :M -.184(algorithm )A 369 386 :M -.082(gets )A 392 386 :M -.22(the )A 410 386 :M -.132(right )A 436 386 :M -.15(relationship)A 59 410 :M -.132(among )A 95 410 :M -.22(the )A 113 410 :M -.047(subtest )A 150 410 :M (scores )S 184 410 :M -.109(and )A 205 410 :M -.22(the )A 223 410 :M -.332(AFQT )A 257 410 :M .43 .043(score, )J 290 410 :M -.334(it )A 301 410 :M -.082(gets )A 325 410 :M -.22(the )A 344 410 :M .229 .023(wrong )J 380 410 :M -.137(relationship )A 440 410 :M -.132(among )A 477 410 :M -.33(the)A 59 434 :M -.069(subtest scores. This was evident because the PC algorithm output a )A 380 434 :M -.188(pattern )A 416 434 :M -.249(that )A 437 434 :M -.129(represented)A 59 458 :M -.087(graphs that had )A 135 458 :M -.326(a )A 144 458 :M -.052(cycle, )A 176 458 :M -.065(which )A 209 458 :M (does )S 235 458 :M -.111(not )A 254 458 :M -.247(make )A 283 458 :M -.09(substantive )A 340 458 :M (sense )S 370 458 :M -.167(in )A 383 458 :M -.084(this )A 404 458 :M .236 .024(case. )J 432 458 :M -.083(This )A 457 458 :M (is )S 469 458 :M .087(true.)A 59 482 :M .571 .057(However, )J 113 482 :M -.084(this )A 136 482 :M -.21(application )A 193 482 :M (of )S 209 482 :M -.22(the )A 229 482 :M -.184(algorithm )A 280 482 :M -.046(assumed )A 327 482 :M -.098(linearity. )A 375 482 :M -.219(The )A 399 482 :M -.137(relationship )A 460 482 :M (of )S 477 482 :M -.33(the)A 59 506 :M -.1(component scores to the AFQT score \(as )A 258 506 :M -.263(calculated )A 308 506 :M -.167(in )A 321 506 :M (1987\) )S 353 506 :M (is )S 365 506 :M f2_12 sf .305(known)A f1_12 sf .146 .015( )J 402 506 :M -.167(to )A 415 506 :M -.163(be )A 430 506 :M -.045(linear. )A 464 506 :M -.244(There)A 59 530 :M (is )S 71 530 :M (no )S 87 530 :M -.052(reason )A 122 530 :M -.33(at )A 134 530 :M -.331(all )A 149 530 :M -.167(to )A 162 530 :M -.235(believe )A 199 530 :M -.249(that )A 220 530 :M -.22(the )A 238 530 :M -.137(relationship )A 297 530 :M -.132(among )A 334 530 :M -.22(the )A 353 530 :M -.047(subtest )A 391 530 :M (scores )S 426 530 :M (is )S 439 530 :M -.045(linear. )A 474 530 :M .665(So,)A 59 554 :M -.108(where the )A 109 554 :M -.142(distributional )A 175 554 :M -.03(assumptions )A 238 554 :M -.215(are )A 256 554 :M .224 .022(known )J 293 554 :M -.167(to )A 306 554 :M -.163(be )A 321 554 :M -.037(correct, )A 361 554 :M -.22(the )A 379 554 :M -.184(algorithm )A 428 554 :M -.082(gets )A 451 554 :M -.22(the )A 469 554 :M -.165(right)A 59 578 :M .602 .06(answer, )J 102 578 :M -.109(and )A 124 578 :M -.062(where )A 158 578 :M -.196(there )A 186 578 :M .264 .026(was )J 210 578 :M (no )S 227 578 :M -.052(reason )A 264 578 :M -.167(to )A 279 578 :M -.235(believe )A 318 578 :M -.249(that )A 341 578 :M -.22(the )A 361 578 :M -.066(assumption )A 421 578 :M (is )S 435 578 :M -.037(correct, )A 477 578 :M -.33(the)A 59 602 :M -.041(algorithm gets the wrong answer.)A 59 626 :M f0_12 sf 2.488 .249(4.3 Smoking and Lung Cancer:)J 59 650 :M f1_12 sf -.157(According to Freedman:)A endp %%Page: 16 16 %%BeginPageSetup initializepage (peter; page: 16 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 77 50 :M f1_12 sf 2.308 .231(... )J 94 50 :M (does )S 121 50 :M -.048(smoking )A 167 50 :M -.129(cause )A 198 50 :M -.083(lung )A 224 50 :M -.043(cancer, )A 263 50 :M -.196(heart )A 291 50 :M .196 .02(disease, )J 334 50 :M -.109(and )A 356 50 :M -.165(many )A 387 50 :M -.131(other )A 416 50 :M .168(illnesses?...)A 77 74 :M -.163(When )A 109 74 :M -.165(they )A 133 74 :M -.248(actually )A 173 74 :M -.22(get )A 191 74 :M .24 .024(down )J 222 74 :M -.167(to )A 235 74 :M -.093(arguing )A 275 74 :M -.197(their )A 301 74 :M .236 .024(case, )J 330 74 :M -.165(they )A 355 74 :M .672 .067([SGS] )J 391 74 :M (use )S 412 74 :M -.326(a )A 422 74 :M -.162(rather )A 454 74 :M -.109(old-)A 77 98 :M -.072(fashioned )A 128 98 :M -.123(method-- )A 176 98 :M -.326(a )A 186 98 :M -.23(literature )A 232 98 :M -.107(review )A 269 98 :M -.083(with )A 295 98 :M -.109(arguments )A 350 98 :M -.167(in )A 365 98 :M -.081(ordinary )A 411 98 :M -.095(English )A 453 98 :M .336(\(pp.)A 77 122 :M -.032(291-302\). Causal models and search algorithms have disappeared. \(Freedman, 26\).)A 77 170 :M .765 .077(SGS )J 107 170 :M -.282(elected )A 146 170 :M -.111(not )A 168 170 :M -.167(to )A 184 170 :M (use )S 207 170 :M -.197(their )A 235 170 :M -.264(analytical )A 286 170 :M -.182(machinery )A 342 170 :M (on )S 362 170 :M -.22(the )A 384 170 :M -.048(smoking )A 433 170 :M -.162(data-- )A 468 170 :M (a)S 77 194 :M -.007(remarkable omission. \(Freedman, 27\).)A 59 242 :M -.219(The )A 81 242 :M -.111(output )A 115 242 :M (of )S 129 242 :M -.326(a )A 138 242 :M -.106(search )A 172 242 :M -.184(algorithm )A 221 242 :M (is )S 233 242 :M -.109(one )A 254 242 :M -.083(kind )A 279 242 :M (of )S 293 242 :M -.205(evidence )A 338 242 :M (for )S 356 242 :M -.326(a )A 365 242 :M -.163(causal )A 398 242 :M -.109(claim, )A 431 242 :M -.111(but )A 450 242 :M -.196(there )A 477 242 :M -.323(are)A 59 266 :M .4 .04(others. )J 96 266 :M -.326(We )A 116 266 :M (discussed )S 166 266 :M -.082(some )A 195 266 :M (of )S 209 266 :M -.249(them )A 236 266 :M -.167(in )A 249 266 :M -.22(the )A 267 266 :M -.161(case )A 291 266 :M (of )S 305 266 :M -.048(smoking )A 350 266 :M -.109(and )A 372 266 :M -.083(lung )A 398 266 :M -.043(cancer. )A 437 266 :M -.219(The )A 460 266 :M -.062(reason)A 59 290 :M -.249(that )A 80 290 :M (we )S 98 290 :M (discussed )S 148 290 :M -.22(the )A 166 290 :M -.048(smoking )A 211 290 :M -.109(and )A 232 290 :M -.083(lung )A 257 290 :M -.216(cancer )A 291 290 :M -.161(case )A 315 290 :M -.167(in )A 328 290 :M -.081(ordinary )A 372 290 :M -.095(English )A 412 290 :M .264 .026(was )J 435 290 :M -.139(because )A 477 290 :M (we)S 59 314 :M -.159(felt a historical account of that )A 204 314 :M -.161(case )A 228 314 :M -.197(concretely )A 280 314 :M -.18(illustrated )A 330 314 :M .259 .026(how )J 355 314 :M -.22(the )A 373 314 :M .212 .021(issues )J 406 314 :M -.131(concerning )A 462 314 :M -.196(causal)A 59 338 :M -.181(inference )A 106 338 :M -.08(from )A 133 338 :M -.126(observational )A 200 338 :M (data, )S 227 338 :M -.109(and )A 249 338 :M -.165(prediction )A 301 338 :M (of )S 316 338 :M -.22(the )A 335 338 :M -.138(effects )A 371 338 :M (of )S 386 338 :M -.165(intervention )A 447 338 :M -.109(had )A 469 338 :M -.217(been)A 59 362 :M -.136(dealt with by the )A 141 362 :M -.211(statistical )A 188 362 :M -.066(community. )A 249 362 :M -.122(Freedman )A 300 362 :M -.071(disagrees )A 348 362 :M -.083(with )A 373 362 :M -.082(some )A 402 362 :M (of )S 416 362 :M (our )S 436 362 :M .034(discussions)A 59 386 :M (of )S 74 386 :M -.22(the )A 93 386 :M -.071(evidence. )A 143 386 :M -.219(The )A 166 386 :M -.218(relevance )A 216 386 :M (of )S 232 386 :M -.109(any )A 255 386 :M (of )S 271 386 :M -.084(this )A 294 386 :M -.167(to )A 309 386 :M -.22(the )A 329 386 :M -.083(question )A 375 386 :M (of )S 391 386 :M -.22(the )A 411 386 :M -.241(reliability )A 461 386 :M (of )S 477 386 :M -.33(the)A 59 410 :M -.019(algorithms we propose escapes us.)A 59 434 :M -.12(We did not apply the algorithms to smoking and lung cancer data because )A 409 434 :M (we )S 427 434 :M -.122(happened )A 476 434 :M -.167(not)A 59 458 :M -.167(to )A 74 458 :M .592 .059(possess )J 117 458 :M -.109(any )A 140 458 :M (such )S 168 458 :M (data. )S 197 458 :M -.19(Without )A 241 458 :M -.22(the )A 261 458 :M (data, )S 290 458 :M (we )S 310 458 :M (do )S 328 458 :M -.111(not )A 349 458 :M .24 .024(know )J 383 458 :M -.065(which )A 419 458 :M -.145(variables )A 468 458 :M -.103(were)A 59 482 :M -.043(measured, how they are )A 176 482 :M -.027(distributed, )A 234 482 :M (etc. )S 255 482 :M -.186(Whether )A 299 482 :M -.22(the )A 317 482 :M -.132(algorithms )A 371 482 :M -.215(are )A 389 482 :M -.231(applicable )A 440 482 :M -.109(and )A 461 482 :M (would)S 59 506 :M -.092(produce )A 101 506 :M -.163(an )A 116 506 :M -.15(interesting )A 169 506 :M -.109(result )A 200 506 :M -.046(depends )A 244 506 :M (upon )S 273 506 :M -.22(the )A 292 506 :M .21 .021(answers )J 336 506 :M -.167(to )A 350 506 :M -.131(these )A 379 506 :M .336 .034(questions. )J 433 506 :M -.113(But )A 455 506 :M -.196(there )A 483 506 :M (is)S 59 530 :M -.118(nothing in principle that prevents the application of the algorithms to such data.)A 59 554 :M f0_12 sf 3.082 .308(4.4 The Rindfuss Example)J 59 578 :M f1_12 sf -.085(Freedman points out there were some errors in the covariance matrix we used. )A 432 578 :M (He )S 450 578 :M (does )S 476 578 :M -.167(not)A 59 602 :M -.102(point out that those errors make no difference in the output of the algorithm.)A 59 626 :M f0_12 sf 4.847 .485(5. Conclusion)J 59 650 :M f1_12 sf -.106(Much of applied statistics is devoted to drawing causal conclusion from )A 400 650 :M -.211(statistical )A 447 650 :M (data. )S 474 650 :M -.169(But)A 59 674 :M -.111(when examining causal inferences, statisticians all too often simply trot out )A 416 674 :M -.326(a )A 425 674 :M (few )S 447 674 :M -.188(examples)A endp %%Page: 17 17 %%BeginPageSetup initializepage (peter; page: 17 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.12(of circumstances under which particular causal inferences )A 334 50 :M -.164(cannot )A 369 50 :M -.163(be )A 384 50 :M (made. )S 417 50 :M -.247(What )A 446 50 :M (is )S 458 50 :M -.196(needed)A 59 74 :M (is )S 71 74 :M -.326(a )A 80 74 :M (rigorous )S 124 74 :M -.21(examination )A 185 74 :M (of )S 199 74 :M -.081(what )A 226 74 :M -.163(causal )A 259 74 :M -.146(relations )A 303 74 :M -.217(can )A 323 74 :M -.163(be )A 338 74 :M -.121(inferred )A 379 74 :M -.132(given )A 409 74 :M -.093(varying )A 450 74 :M (kinds )S 481 74 :M (of)S 59 98 :M -.065(background )A 119 98 :M .175 .018(knowledge. )J 179 98 :M -.247(What )A 208 98 :M -.132(could )A 238 98 :M (we )S 256 98 :M -.129(infer )A 282 98 :M -.132(about )A 312 98 :M -.163(causal )A 345 98 :M -.108(structure )A 390 98 :M -.164(if )A 402 98 :M (we )S 421 98 :M (knew )S 452 98 :M -.22(the )A 471 98 :M -.443(time)A 59 122 :M -.093(order of the variables? What if we knew no )A 267 122 :M -.166(common )A 312 122 :M -.052(causes )A 347 122 :M -.077(were )A 374 122 :M -.235(acting? )A 411 122 :M -.247(What )A 440 122 :M -.164(if )A 451 122 :M (we )S 469 122 :M -.217(have)A 59 146 :M -.098(measured a large number of variables? In addition, )A 302 146 :M -.196(there )A 329 146 :M (should )S 365 146 :M -.163(be )A 380 146 :M -.326(a )A 389 146 :M -.109(theory )A 423 146 :M -.132(about )A 453 146 :M (when )S 483 146 :M (is)S 59 170 :M -.091(it possible )A 111 170 :M -.167(to )A 124 170 :M -.219(determine )A 174 170 :M -.22(the )A 192 170 :M -.138(effects )A 227 170 :M (of )S 241 170 :M -.163(an )A 256 170 :M -.165(intervention )A 316 170 :M (upon )S 344 170 :M -.249(that )A 365 170 :M -.163(causal )A 398 170 :M (structure, )S 447 170 :M -.132(given )A 477 170 :M -.33(the)A 59 194 :M -.095(inferences that can be made about causal structure. CPS )A 326 194 :M -.207(attempts )A 369 194 :M -.167(to )A 382 194 :M -.189(systematically )A 452 194 :M -.274(examine)A 59 218 :M -.059(these kinds of questions. Under a variety of assumptions there are positive results )A 449 218 :M -.249(that )A 470 218 :M -.247(state)A 59 242 :M (when )S 90 242 :M (two )S 113 242 :M -.144(different )A 158 242 :M -.163(causal )A 192 242 :M -.064(structures )A 243 242 :M -.217(can )A 264 242 :M -.163(be )A 280 242 :M -.077(distinguished )A 348 242 :M -.132(given )A 380 242 :M -.22(the )A 400 242 :M (data, )S 429 242 :M -.109(and )A 452 242 :M -.235(negative)A 59 266 :M -.046(results )A 94 266 :M -.249(that )A 115 266 :M -.197(state )A 140 266 :M (when )S 170 266 :M -.165(they )A 194 266 :M (cannot. )S 233 266 :M -.195(There )A 264 266 :M (is )S 276 266 :M -.326(a )A 286 266 :M -.165(systematic )A 340 266 :M -.21(examination )A 402 266 :M (of )S 417 266 :M -.22(the )A 436 266 :M -.15(relationship)A 59 290 :M -.139(between )A 103 290 :M -.235(partial )A 137 290 :M -.072(knowledge )A 194 290 :M -.132(about )A 225 290 :M -.163(causal )A 259 290 :M -.064(structures )A 310 290 :M -.109(and )A 332 290 :M -.081(what )A 360 290 :M -.217(can )A 381 290 :M -.163(be )A 397 290 :M -.182(predicted )A 445 290 :M -.132(about )A 477 290 :M -.33(the)A 59 314 :M -.138(effects )A 97 314 :M (of )S 114 314 :M -.075(intervention. )A 181 314 :M -.164(It )A 195 314 :M (is )S 210 314 :M -.111(not )A 232 314 :M -.109(complete, )A 285 314 :M -.109(and )A 309 314 :M -.196(there )A 339 314 :M -.22(may )A 366 314 :M -.163(be )A 384 314 :M -.165(many )A 417 314 :M -.131(other )A 448 314 :M (kinds )S 481 314 :M (of)S 59 338 :M -.03(assumptions )A 122 338 :M -.249(that )A 143 338 :M (should )S 179 338 :M -.163(be )A 194 338 :M -.075(investigated, )A 258 338 :M -.111(but )A 277 338 :M (we )S 295 338 :M -.134(think )A 323 338 :M -.249(that )A 344 338 :M -.334(it )A 354 338 :M (is )S 366 338 :M -.163(an )A 381 338 :M -.235(example )A 424 338 :M (of )S 438 338 :M -.22(the )A 456 338 :M -.083(kind )A 481 338 :M (of)S 59 362 :M -.11(research into causal inference that should be an important part of statistics.)A 59 386 :M -.219(The )A 84 386 :M -.129(space )A 117 386 :M (of )S 135 386 :M -.041(possible )A 182 386 :M -.163(causal )A 219 386 :M .199 .02(models, )J 265 386 :M -.163(even )A 295 386 :M (when )S 329 386 :M -.165(many )A 363 386 :M -.163(have )A 393 386 :M -.163(been )A 423 386 :M -.265(eliminated )A 479 386 :M (by)S 59 410 :M -.051(background knowledge, is far too large )A 249 410 :M -.167(to )A 262 410 :M -.106(search )A 296 410 :M -.095(without )A 336 410 :M -.22(automated )A 388 410 :M .226 .023(help. )J 416 410 :M -.33(One )A 439 410 :M -.163(part )A 461 410 :M (of )S 475 410 :M (our)S 59 434 :M -.188(project )A 97 434 :M .264 .026(was )J 122 434 :M -.22(the )A 142 434 :M -.04(proposal )A 189 434 :M (of )S 205 434 :M -.082(some )A 236 434 :M -.132(algorithms )A 292 434 :M -.249(that )A 315 434 :M (use )S 337 434 :M -.211(statistical )A 386 434 :M -.247(data )A 411 434 :M -.109(and )A 435 434 :M -.072(background)A 59 458 :M -.072(knowledge )A 115 458 :M -.083(supplied )A 159 458 :M (by )S 175 458 :M -.326(a )A 184 458 :M (user )S 208 458 :M -.167(to )A 221 458 :M (suggest )S 261 458 :M -.163(causal )A 295 458 :M -.11(models )A 334 458 :M -.231(compatible )A 390 458 :M -.083(with )A 416 458 :M -.22(the )A 435 458 :M -.072(background)A 59 482 :M -.075(knowledge and )A 135 482 :M -.22(the )A 153 482 :M (data. )S 180 482 :M -.165(As )A 197 482 :M (we )S 215 482 :M -.163(have )A 241 482 :M -.11(consistently )A 301 482 :M -.164(emphasized )A 360 482 :M -.123(\(despite )A 401 482 :M .598 .06(Freedman's )J 461 482 :M -.264(claims)A 59 506 :M -.126(to the contrary\) it is an empirical question whether )A 299 506 :M -.22(the )A 317 506 :M -.132(algorithms )A 371 506 :M -.215(are )A 389 506 :M -.247(reliable )A 427 506 :M (when )S 457 506 :M -.22(applied)A 59 530 :M -.167(to )A 72 530 :M -.245(real )A 93 530 :M (data. )S 120 530 :M -.164(Even )A 148 530 :M -.164(if )A 159 530 :M -.22(the )A 177 530 :M -.132(algorithms )A 231 530 :M -.215(are )A 249 530 :M -.053(useful )A 283 530 :M -.167(in )A 297 530 :M -.107(practice, )A 342 530 :M -.179(informative )A 401 530 :M -.109(and )A 423 530 :M -.247(reliable )A 462 530 :M -.196(causal)A 59 554 :M -.181(inference )A 106 554 :M -.08(from )A 133 554 :M -.202(correlational )A 195 554 :M -.247(data )A 218 554 :M -.166(will )A 240 554 :M -.111(not )A 259 554 :M -.163(be )A 274 554 :M .454 .045(easy. )J 303 554 :M -.219(The )A 325 554 :M -.132(right )A 351 554 :M -.145(variables )A 398 554 :M -.084(must )A 426 554 :M -.163(be )A 442 554 :M (measured,)S 59 578 :M -.103(they have to be distributed in such )A 224 578 :M -.326(a )A 233 578 :M (way )S 257 578 :M -.249(that )A 278 578 :M -.13(reasonable )A 332 578 :M -.066(tests )A 357 578 :M (of )S 371 578 :M -.181(conditional )A 427 578 :M -.179(independence)A 59 602 :M -.081(can be made, and )A 145 602 :M -.22(the )A 163 602 :M -.163(causal )A 196 602 :M -.101(relationships )A 260 602 :M -.132(among )A 296 602 :M -.22(the )A 314 602 :M -.145(variables )A 360 602 :M -.164(cannot )A 395 602 :M -.163(be )A 410 602 :M -.111(too )A 429 602 :M -.04(complex. )A 477 602 :M -.666(All)A 59 626 :M -.092(of these caveats are clear in our book and emphasized in Glymour \(this volume\).)A 59 650 :M -.14(There are three kinds of evidence concerning the reliability of )A 351 650 :M -.22(the )A 369 650 :M -.029(algorithms. )A 427 650 :M (First )S 453 650 :M -.165(they )A 477 650 :M -.323(are)A 59 674 :M -.189(asymptotically )A 131 674 :M -.186(correct )A 167 674 :M -.132(given )A 197 674 :M -.22(the )A 215 674 :M -.03(assumptions )A 278 674 :M (we )S 297 674 :M (make. )S 331 674 :M .398 .04(Second, )J 375 674 :M -.166(simulation )A 429 674 :M -.066(tests )A 455 674 :M -.283(indicate)A endp %%Page: 18 18 %%BeginPageSetup initializepage (peter; page: 18 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 50 :M f1_12 sf -.249(that )A 81 50 :M (when )S 112 50 :M -.22(the )A 131 50 :M -.166(modeling )A 180 50 :M -.03(assumptions )A 244 50 :M -.215(are )A 263 50 :M (satisfied, )S 311 50 :M -.109(and )A 333 50 :M -.22(the )A 352 50 :M -.165(sample )A 391 50 :M -.064(sizes )A 420 50 :M -.215(are )A 440 50 :M -.108(reasonably)A 59 74 :M -.098(large, they are reliable. Third, there is some evidence from application to real data sets.)A 59 98 :M -.219(The )A 81 98 :M -.205(evidence )A 126 98 :M -.08(from )A 153 98 :M -.21(application )A 208 98 :M -.167(to )A 221 98 :M -.245(real )A 242 98 :M -.247(data )A 265 98 :M (sets )S 287 98 :M (is )S 299 98 :M -.22(the )A 317 98 :M -.084(most )A 344 98 :M -.052(fragmentary. )A 409 98 :M -.326(We )A 429 98 :M -.182(generally )A 476 98 :M -.167(did)A 59 122 :M -.111(not )A 79 122 :M -.163(have )A 106 122 :M -.106(access )A 141 122 :M -.167(to )A 155 122 :M (raw )S 178 122 :M (data, )S 206 122 :M -.109(and )A 228 122 :M -.167(in )A 242 122 :M -.084(most )A 270 122 :M -.062(cases )A 301 122 :M (we )S 321 122 :M (do )S 339 122 :M -.111(not )A 360 122 :M .24 .024(know )J 393 122 :M -.092(whether )A 437 122 :M -.22(the )A 457 122 :M .055(output,)A 59 146 :M -.044(however )A 104 146 :M -.13(reasonable )A 158 146 :M -.334(it )A 168 146 :M -.22(may )A 192 146 :M .231 .023(seem, )J 224 146 :M (is )S 236 146 :M -.037(correct. )A 277 146 :M (In )S 292 146 :M -.22(the )A 311 146 :M -.332(AFQT )A 346 146 :M .236 .024(case, )J 375 146 :M -.132(among )A 412 146 :M -.22(the )A 431 146 :M -.11(relationships)A 59 170 :M .224 .022(known )J 97 170 :M -.167(to )A 111 170 :M -.163(be )A 127 170 :M -.045(linear, )A 162 170 :M -.334(it )A 173 170 :M -.111(output )A 208 170 :M -.163(an )A 224 170 :M (answer )S 263 170 :M .224 .022(known )J 301 170 :M -.167(to )A 315 170 :M -.163(be )A 332 170 :M -.037(correct. )A 374 170 :M (In )S 390 170 :M -.22(the )A 410 170 :M -.161(case )A 436 170 :M (of )S 452 170 :M -.141(Spartina)A 59 194 :M -.047(biomass )A 102 194 :M .359 .036(\(Spirtes, )J 147 194 :M -.046(Glymour )A 194 194 :M -.109(and )A 216 194 :M -.081(Scheines )A 263 194 :M .667 .067(1993, )J 296 194 :M .533 .053(244-248\), )J 349 194 :M -.22(the )A 368 194 :M -.184(algorithm )A 418 194 :M -.197(again )A 448 194 :M -.205(predicted)A 59 218 :M -.092(from observational data results confirmed by experiment. In a number of )A 406 218 :M -.131(other )A 434 218 :M -.164(examples )A 482 218 :M -.334(in)A 59 242 :M -.058(CPS that were not )A 149 242 :M (discussed )S 199 242 :M (by )S 215 242 :M (Freedman, )S 270 242 :M -.22(the )A 288 242 :M .21 .021(answers )J 331 242 :M -.162(appeared )A 377 242 :M -.027(reasonable, )A 435 242 :M -.111(but )A 454 242 :M -.334(it )A 464 242 :M (is )S 476 242 :M -.167(not)A 59 266 :M .224 .022(known )J 96 266 :M -.092(whether )A 138 266 :M -.165(they )A 162 266 :M -.215(are )A 180 266 :M -.037(correct. )A 220 266 :M -.247(More )A 249 266 :M -.146(extensive )A 297 266 :M -.165(applications )A 357 266 :M -.166(will )A 380 266 :M -.093(provide )A 421 266 :M -.163(more )A 450 266 :M -.234(evidence)A 59 290 :M -.165(about the reliability of the )A 183 290 :M -.132(algorithms )A 237 290 :M -.167(to )A 250 290 :M -.245(real )A 271 290 :M -.247(data )A 294 290 :M .67 .067(sets. )J 320 290 :M -.326(We )A 340 290 :M -.215(are )A 358 290 :M -.145(currently )A 404 290 :M -.122(carrying )A 447 290 :M -.111(out )A 466 290 :M -.109(some)A 59 314 :M -.122(applications of the algorithms to medical databases.)A endp %%Page: 19 19 %%BeginPageSetup initializepage (peter; page: 19 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 244 50 :M f0_12 sf .672(References)A 59 68 :M f1_12 sf .257 .026(Frydenberg, M. \(1990\). "The Chain Graph Markov Property." )J f2_12 sf .247 .025(Scand. J. Statist,)J f1_12 sf ( )S f0_12 sf .071(17)A f1_12 sf .22 .022(, 333-)J 77 86 :M .333(353.)A 59 104 :M -.006(Heckerman, D., Geiger, D., and Chickering, D. \(1994\) Learning Bayesian Networks: The)A 77 122 :M -.104(Combination of Knowledge and Statistical Data, Technical Report MSR-TR-94-09,)A 77 140 :M -.087(Microsoft Research, Advanced Technology Division, Redmond WA.)A 59 170 :M .375 .037(Spirtes, )J 101 170 :M 1.792 .179(P., )J 121 170 :M .375 .038(Glymour, )J 173 170 :M 1.535 .154(C., )J 194 170 :M -.334(& )A 208 170 :M .184 .018(Scheines, )J 259 170 :M .83 .083(R. )J 276 170 :M .596 .06(\(1993\). )J 317 170 :M ( )S 322 170 :M (Causation, )S 378 170 :M -.059(prediction, )A 434 170 :M -.109(and )A 457 170 :M .06(search.)A 77 188 :M -.022(Lecture Notes in Statistics, 81, Spring-Verlag, New York.)A 59 218 :M -.023(Verma, T. and )A 132 218 :M .219 .022(Pearl, )J 164 218 :M 1.111 .111(J. )J 177 218 :M .596 .06(\(1990\). )J 217 218 :M -.209(Equivalence )A 278 218 :M -.109(and )A 299 218 :M (synthesis )S 347 218 :M (of )S 361 218 :M -.163(causal )A 394 218 :M .199 .02(models. )J 436 218 :M .673 .067(Proc. )J 466 218 :M -.085(Sixth)A 77 236 :M -.13(Conference )A 135 236 :M (on )S 151 236 :M -.149(Uncertainty )A 210 236 :M -.167(in )A 223 236 :M .264 .026(AI. )J 244 236 :M -.15(Association )A 304 236 :M (for )S 323 236 :M -.149(Uncertainty )A 383 236 :M -.167(in )A 397 236 :M .264 .026(AI, )J 418 236 :M 1.12 .112(Inc., )J 446 236 :M -.237(Mountain)A 77 254 :M .366 .037(View, CA, 220-227.)J endp %%Page: 20 20 %%BeginPageSetup initializepage (peter; page: 20 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 64 41 421 19 rC 68 54 :M f2_12 sf .077 .008(X Y Z W)J 10 156 204 125 50 @k 86 51 -1 1 117 50 1 86 50 @a 10 156 204 236 50 @k 197 51 -1 1 228 50 1 197 50 @a 10 -24 24 143 50 @k 150 51 -1 1 181 50 1 150 50 @a 290 53 :M .077 .008(X Y Z W)J 10 156 204 347 49 @k 308 50 -1 1 339 49 1 308 49 @a 10 -24 24 420 49 @k 427 50 -1 1 458 49 1 427 49 @a 10 -24 24 365 49 @k 372 50 -1 1 403 49 1 372 49 @a gR gS 0 0 552 730 rC 59 81 :M f1_12 sf -.009( \(i\) \(ii\))A endp %%Page: 21 21 %%BeginPageSetup initializepage (peter; page: 21 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 41 493 21 rC gS 37.665 1.167 scale 101.575 44.143 :T -101.575 -44.143 :T 5.575 47.143 :M f2_12 sf .077 .008(X Y Z W)J gR 156 204 753 23 2356.5 50.5 @l 887 51 -38 1 2055 50 38 887 50 @a 5068 51 -38 1 6537 50 38 5068 50 @a -24 24 754 23 3034 50.5 @l 3298 51 -38 1 4465 50 38 3298 50 @a endp %%Page: 22 22 %%BeginPageSetup initializepage (peter; page: 22 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 53 493 73 rC gS 35.004 1.431 scale 55.685 78.74 :T -55.685 -78.74 :T 5.685 81.74 :M f2_12 sf .125 .013(X Y Z)J gR 156 204 700 29 1773 111.5 @l 794 113 -35 1 1493 112 35 794 112 @a 156 204 699 29 3277.5 111.5 @l 2228 113 -35 1 2998 112 35 2228 112 @a 35 1 180 270 2799 80 1896 99.5 @p -114 -66 699 29 3522.5 100.5 @l -1 -35 3522 90 1 35 3487 84 @b 35 1 -90 0 3428 55 1825.5 85 @p gS 35.004 1.431 scale 206.613 78.74 :T -206.613 -78.74 :T 156.613 81.74 :M f2_12 sf .125 .013(X Y Z)J gR 156 204 700 29 7056 111.5 @l 6076 113 -35 1 6776 112 35 6076 112 @a -24 24 700 29 7546 111.5 @l 7791 113 -35 1 8560 112 35 7791 112 @a gR gS 0 0 552 730 rC 59 147 :M f1_12 sf -.014( \(i\) \(ii\))A endp %%Page: 23 23 %%BeginPageSetup initializepage (peter; page: 23 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 59 41 122 18 rC 63 53 :M f2_12 sf .104 .01(X Y Z)J 10 -24 24 81 49 @k 88 50 -1 1 118 49 1 88 49 @a 10 156 204 168 49 @k 130 50 -1 1 160 49 1 130 49 @a endp %%Page: 24 24 %%BeginPageSetup initializepage (peter; page: 24 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC 214 41 122 18 rC 218 53 :M f2_12 sf .104 .01(X Y Z)J 235 50 -1 1 273 49 1 235 49 @a 285 50 -1 1 323 49 1 285 49 @a gR gS 0 0 552 730 rC 269 80 :M f1_12 sf -.16(\(i\))A 59 107 493 32 rC gS 27.819 1.778 scale 63.111 69 :T -63.111 -69 :T 6.111 72 :M f2_12 sf .104 .01(X Y Z)J gR 156 204 556 36 1699 121 @l 643 123 -28 2 1477 121 28 643 121 @a 156 204 556 36 3089 121 @l 2033 123 -28 2 2867 121 28 2033 121 @a gS 27.819 1.778 scale 196.004 69 :T -196.004 -69 :T 139.004 72 :M f2_12 sf .104 .01(X Y Z)J gR -24 24 556 36 4368 121 @l 4562 123 -28 2 5397 121 28 4562 121 @a 156 204 556 36 6786 121 @l 5730 123 -28 2 6564 121 28 5730 121 @a gS 27.819 1.778 scale 328.933 69 :T -328.933 -69 :T 271.933 72 :M f2_12 sf .104 .01(X Y Z)J gR -24 24 556 36 8065 121 @l 8260 123 -28 2 9094 121 28 8260 121 @a 156 204 556 36 10484 121 @l 9427 123 -28 2 10261 121 28 9427 121 @a gR gS 0 0 552 730 rC 59 160 :M f1_12 sf -.017( \(ii\) \(iii\) \(iv\))A endp %%Page: 25 25 %%BeginPageSetup initializepage (peter; page: 25 of 25)setjob %%EndPageSetup gS 0 0 552 730 rC endp %%Trailer end %%EOF