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y(that)e(are)g(\\nearly)g(singly-connected,")j(it)d(seems)h(unlik)o (ely)h(to)e(pro)o(vide)h(a)f(solution)h(for)f(dense)h(graphs)75 576 y(suc)o(h)k(as)g(the)g(QMR-DT.)f(In)i(particular,)g(the)e(median)i (cutset)f(size)h(for)e(the)h(QMR-DT)g(across)f(the)75 632 y(CPC)c(cases)h(is)h(106.5,)d(yielding)k(an)e(unmanageably)g(large) g(n)o(um)o(b)q(er)h(of)e(2)1362 616 y Ft(106)p Fj(:)p Ft(5)1459 632 y Fm(cutset)h(instan)o(tiations.)146 691 y(Another)21 b(approac)o(h)h(to)f(appro)o(ximate)g(inference)j(is)e (pro)o(vided)h(b)o(y)f(\\searc)o(h-based")f(metho)q(ds,)75 747 y(whic)o(h)e(consider)f(no)q(de)h(instan)o(tiations)f(across)f(the) h(en)o(tire)g(graph)g(\(Co)q(op)q(er,)g(1985;)f(Henrion,)i(1991;)75 804 y(P)o(eng)13 b(&)g(Reggia,)g(1987\).)18 b(The)13 b(general)h(hop)q(e)f(in)h(these)f(metho)q(ds)g(is)h(that)e(a)g (relativ)o(ely)i(small)g(fraction)75 860 y(of)e(the)g(\(exp)q(onen)o (tially)i(man)o(y\))d(no)q(de)i(instan)o(tiations)f(con)o(tains)g(a)g 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y(Henrion)f(\(1991\))d(w)o(as)i(in)h(fact)e(able)i(to)f(run)g(a)g (searc)o(h-based)h(algorithm)f(on)g(the)g(QMR-DT)g(inference)75 1312 y(problem,)j(for)e(a)h(set)g(of)g(cases)g(c)o(haracterized)h(b)o (y)f(a)f(small)i(n)o(um)o(b)q(er)g(of)f(diseases.)23 b(These)17 b(w)o(ere)e(cases,)75 1368 y(ho)o(w)o(ev)o(er,)f(for)h(whic) o(h)h(the)f(exact)g(Quic)o(kscore)i(algorithm)e(is)h(e\016cien)o(t.)21 b(The)15 b(more)g(general)h(corpus)f(of)75 1425 y(CPC)h(cases)g(that)f (w)o(e)h(discuss)h(in)g(the)f(curren)o(t)g(pap)q(er)g(is)h(not)f(c)o (haracterized)g(b)o(y)g(a)g(small)h(n)o(um)o(b)q(er)f(of)75 1481 y(diseases)e(p)q(er)g(case.)19 b(In)14 b(general,)g(ev)o(en)f(if)h (w)o(e)f(imp)q(ose)h(the)g(assumption)f(that)g(patien)o(ts)g(ha)o(v)o (e)g(a)g(limited)75 1538 y(n)o(um)o(b)q(er)k Fi(N)k Fm(of)16 b(diseases,)i(w)o(e)e(cannot)h(assume)f(a)h(priori)g(that)f(the)h(mo)q (del)g(will)i(sho)o(w)d(a)g(sharp)h(cuto\013)75 1594 y(in)g(p)q(osterior)f(probabilit)o(y)h(after)f(disease)h Fi(N)5 b Fm(.)22 b(Finally)l(,)17 b(in)g(high-dimensional)i(searc)o(h)d (problems)h(it)f(is)75 1650 y(often)i(necessary)h(to)e(allo)o(w)i (paths)f(that)f(are)i(not)e(limited)k(to)c(the)i(target)e(h)o(yp)q (othesis)i(subspace;)h(in)75 1707 y(particular,)f(one)f(w)o(ould)g(lik) o(e)h(to)f(b)q(e)g(able)h(to)e(arriv)o(e)h(at)f(a)h(h)o(yp)q(othesis)h (con)o(taining)g(few)e(diseases)i(b)o(y)75 1763 y(pruning)c(h)o(yp)q (otheses)f(con)o(taining)h(additional)g(diseases)g(\(P)o(eng)e(&)h (Reggia,)g(1987\).)k(Imp)q(osing)d(suc)o(h)f(a)75 1820 y(limitation)j(can)e(lead)h(to)e(failure)j(of)d(the)i(searc)o(h.)146 1878 y(More)9 b(recen)o(t)h(partial)h(ev)m(aluation)g(metho)q(ds)f (include)j(the)d(\\lo)q(calized)i(partial)f(ev)m(aluation")g(metho)q(d) 75 1935 y(of)17 b(Drap)q(er)g(and)g(Hanks)g(\(1994\),)f(the)h (\\incremen)o(tal)h(SPI")g(algorithm)f(of)g(D'Am)o(brosio)f(\(1993\),)g (the)75 1991 y(\\probabilistic)d(partial)f(ev)m(aluation")h(metho)q(d)e 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y(graphical)f(in)o(terpretation)f(in)i(the)e (case)g(of)g(the)g(QMR-DT.)146 650 y(A)i(\014nal)h(class)f(of)g(metho)q (ds)g(for)g(p)q(erforming)h(appro)o(ximate)e(inference)j(are)e(the)g (sto)q(c)o(hastic)g(sam-)75 706 y(pling)e(metho)q(ds.)20 b(Sto)q(c)o(hastic)14 b(sampling)h(is)f(a)g(large)f(family)l(,)i (including)i(tec)o(hniques)e(suc)o(h)f(as)f(rejection)75 762 y(sampling,)j(imp)q(ortance)g(sampling,)g(and)f(Mark)o(o)o(v)f(c)o (hain)i(Mon)o(te)e(Carlo)h(metho)q(ds)h(\(MacKa)o(y)l(,)e(1998\).)75 819 y(Man)o(y)h(of)h(these)g(metho)q(ds)g(ha)o(v)o(e)g(b)q(een)h (applied)h(to)e(the)g(problem)g(of)g(appro)o(ximate)g(probabilistic)i (in-)75 875 y(ference)h(for)e(graphical)i(mo)q(dels)g(and)f(analytic)h (results)f(are)g(a)o(v)m(ailable)h(\(Dagum)e(&)h(Horvitz,)h(1993\).)75 932 y(In)f(particular,)h(Sh)o(w)o(e)f(and)g(Co)q(op)q(er)g(\(1991\))e (prop)q(osed)i(a)f(sto)q(c)o(hastic)h(sampling)h(metho)q(d)f(kno)o(wn)f (as)75 988 y(\\lik)o(eliho)q(o)q(d-w)o(eigh)o(ted)f(sampling")d(for)f 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def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef % setpattern brush of patterns instead of gray /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch extend_font_name def localfont extend_font localfont findfont /xsz f f length 4 sub 4 getinterval cvi def /ysz f f length 8 sub 4 getinterval cvi def [ xsz 0 0 ysz neg 0 0 ] makefont dup f cvn exch def setfont } ifelse } bind def /gfns { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval cvn findfont /xsz f f length 4 sub 4 getinterval cvi def /ysz f f length 8 sub 4 getinterval cvi def [ xsz 0 0 ysz neg 0 0 ] makefont dup f cvn exch def setfont } ifelse } bind def /ul { % space drop thickness gs currentpoint currentlinewidth currentpoint n m 6 -3 roll lw 0 exch r 0 rl st lw m gr } bind def /nxtab { currentpoint pop 1000.0 mul cvi tab mod tab exch sub 1000.0 div 0 rmoveto } bind def /nx { /x exch def } bind def 0. nx gsave 2.83465 -2.83465 scale 0 -279.4 translate topmat currentmatrix pop n 69.361 61.417 m 88.611 82.194 l n 88.611 82.194 m 85.325 80.391 l 87.064 78.78 l cl 0 0 0 F n 69.361 61.417 m 86.194 79.586 l gsave 0 0 0 0.352 0 B grestore n 90.444 63.556 m 90.444 81.583 l n 90.444 81.583 m 89.259 78.027 l 91.63 78.027 l cl 0 0 0 F n 90.444 63.556 m 90.444 78.027 l gsave 0 0 0 0.352 0 B grestore n 68.444 60.5 m 29.944 84.028 l n 29.944 84.028 m 32.361 81.162 l 33.597 83.185 l cl 0 0 0 F n 68.444 60.5 m 32.979 82.174 l gsave 0 0 0 0.352 0 B grestore n 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Ft(3)75 1253 y Fm(In)j(particular:)624 1370 y Fi(f)5 b Fm(\()j Fi(a)h Fm(+)756 1330 y Ff(X)777 1421 y Fj(j)823 1370 y Fi(z)844 1377 y Fj(j)870 1370 y Fm(\))41 b(=)h Fi(f)5 b Fm(\()j Fi(a)i Fm(+)1138 1330 y Ff(X)1160 1421 y Fj(j)1206 1370 y Fi(q)1226 1377 y Fj(j)1249 1339 y Fi(z)1270 1346 y Fj(j)p 1249 1360 40 2 v 1249 1401 a Fi(q)1269 1408 y Fj(j)1301 1370 y Fm(\))475 b(\(11\))929 1498 y Fg(\025)1006 1458 y Ff(X)1028 1549 y Fj(j)1074 1498 y Fi(q)1094 1505 y Fj(j)1120 1498 y Fi(f)5 b Fm(\()j Fi(a)h Fm(+)1257 1468 y Fi(z)1278 1475 y Fj(j)p 1257 1488 V 1257 1530 a Fi(q)1277 1537 y Fj(j)1309 1498 y Fm(\))467 b(\(12\))75 1649 y(where)14 b(the)g Fi(q)302 1656 y Fj(j)335 1649 y Fm(can)g(b)q(e)g(view)o(ed)h(as)f(de\014ning)h(a)f(probabilit)o(y)h (distribution)h(o)o(v)o(er)d(the)h(v)m(ariables)h Fi(z)1746 1656 y Fj(j)1764 1649 y Fm(.)20 b(The)75 1706 y(v)m(ariational)h (parameter)e(in)i(this)f(case)g(is)g(the)g(probabilit)o(y)h (distribution)h Fi(q)r Fm(.)33 b(The)21 b(optimal)f(setting)75 1762 y(of)f(this)g(parameter)f(is)i(giv)o(en)f(b)o(y)g Fi(q)703 1769 y Fj(j)741 1762 y Fm(=)g Fi(z)816 1769 y Fj(j)835 1762 y Fi(=)866 1730 y Ff(P)909 1774 y Fj(k)938 1762 y Fi(z)959 1769 y Fj(k)980 1762 y Fm(.)32 b(This)19 b(is)h(easily)g(v)o(eri\014ed)g(b)o(y)f(substitution)h(in)o(to)75 1819 y(Eq.)15 b(\(12\),)e(and)j(demonstrates)e(that)h(the)g(lo)o(w)o (er)g(b)q(ound)h(is)g(tigh)o(t.)75 1938 y Fr(4.1)26 b(V)l(ariational)19 b(Upp)q(er)f(and)g(Lo)o(w)o(er)e(Bounds)i(for)f(Noisy-OR)75 2021 y Fm(Let)j(us)g(no)o(w)g(return)g(to)f(the)h(problem)h(of)f (computing)g(the)g(p)q(osterior)g(probabilities)j(in)d(the)h(QMR)75 2077 y(mo)q(del.)g(Recall)c(that)d(it)h(is)h(the)f(conditional)i (probabilities)g(corresp)q(onding)f(to)f(the)g(p)q(ositiv)o(e)h (\014ndings)75 2134 y(that)e(need)j(to)d(b)q(e)i(simpli\014ed.)22 b(T)l(o)15 b(this)h(end,)f(w)o(e)g(write)522 2254 y Fi(P)6 b Fm(\()p Fi(f)602 2235 y Ft(+)597 2267 y Fj(i)632 2254 y Fg(j)p Fi(d)p Fm(\))41 b(=)h(1)9 b Fg(\000)i Fi(e)912 2230 y 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b(on)f(the)h(discussion)h (in)f(the)p 75 2530 720 2 v 90 2572 a Fk(3.)f(Jensen's)c(inequalit)o(y) m(,)i(whic)o(h)e(states)f(that)h Fb(f)t Fk(\()p Fb(a)7 b Fk(+)874 2542 y Ff(P)918 2586 y Fe(j)940 2572 y Fb(q)957 2576 y Fe(j)974 2572 y Fb(x)996 2576 y Fe(j)1012 2572 y Fk(\))j Fa(\025)1078 2542 y Ff(P)1122 2586 y Fe(j)1144 2572 y Fb(q)1161 2576 y Fe(j)1178 2572 y Fb(f)t Fk(\()p Fb(a)d Fk(+)g Fb(x)1302 2576 y Fe(j)1318 2572 y Fk(\),)k(for)h(conca)o (v)o(e)h Fb(f)t Fk(,)f(where)1710 2542 y Ff(P)1761 2572 y Fb(q)1778 2576 y Fe(j)1805 2572 y Fk(=)e(1,)137 2627 y(and)k(0)d Fa(\024)f Fb(q)299 2631 y Fe(j)326 2627 y Fa(\024)h Fk(1,)i(is)g(a)g(simple)i(consequence)g(of)d(Eq.)h(\(8\),)g (where)g Fb(x)f Fk(is)i(tak)o(en)g(to)e(b)q(e)i Fb(a)9 b Fk(+)1458 2597 y Ff(P)1502 2640 y Fe(j)1525 2627 y Fb(q)1542 2631 y Fe(j)1558 2627 y Fb(x)1580 2631 y Fe(j)1596 2627 y Fk(.)965 2753 y Fn(8)p eop %%Page: 9 9 9 8 bop 431 -100 a Fq(V)-5 b(aria)m(tional)17 b(Pr)o(obabilistic)e (Inference)h(and)h(QMR-DT)75 124 y Fm(previous)d(section,)h(w)o(e)e (kno)o(w)g(that)g(there)h(m)o(ust)f(exist)h(a)f(v)m(ariational)i(upp)q (er)f(b)q(ound)h(for)e(this)h(function)75 181 y(that)g(is)i(linear)h (in)f Fi(x)p Fm(:)755 286 y Fi(f)5 b Fm(\()p Fi(x)p Fm(\))12 b Fg(\024)h Fi(\030)r(x)d Fg(\000)h Fi(f)1035 268 y Fl(\003)1055 286 y Fm(\()p Fi(\030)r Fm(\))681 b(\(14\))75 392 y(Using)16 b(Eq.)e(\(9\))h(to)f(ev)m(aluate)i(the)g(conjugate)e(function)i Fi(f)1081 376 y Fl(\003)1101 392 y Fm(\()p Fi(\030)r Fm(\))f(for)f(noisy-OR,)j(w)o(e)e(obtain:)578 498 y Fi(f)605 479 y Fl(\003)625 498 y Fm(\()p Fi(\030)r Fm(\))d(=)h Fg(\000)p Fi(\030)d Fm(log)e Fi(\030)k Fm(+)e(\()p Fi(\030)i Fm(+)f(1\))d(log)o(\()p Fi(\030)k Fm(+)f(1\))504 b(\(15\))75 604 y(The)18 b(desired)i(b)q(ound)f(is)g(obtained)g(b)o(y)f (substituting)h(in)o(to)f(Eq.)g(\(13\))f(\(and)h(recalling)i(the)e (de\014nition)75 660 y Fi(x)13 b Fm(=)g Fi(\022)183 667 y Fj(i)p Ft(0)225 660 y Fm(+)270 628 y Ff(P)314 672 y Fj(j)340 660 y Fi(\022)361 667 y Fj(ij)391 660 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1319 1377 mt 1369 1427 L 1369 1377 mt 1319 1427 L 1766 1531 mt 1816 1581 L 1816 1531 mt 1766 1581 L 2212 1539 mt 2262 1589 L 2262 1539 mt 2212 1589 L 2658 1574 mt 2708 1624 L 2708 1574 mt 2658 1624 L 3105 1712 mt 3155 1762 L 3155 1712 mt 3105 1762 L 3551 1861 mt 3601 1911 L 3601 1861 mt 3551 1911 L 3997 1982 mt 4047 2032 L 4047 1982 mt 3997 2032 L 4444 2007 mt 4494 2057 L 4494 2007 mt 4444 2057 L 4890 2123 mt 4940 2173 L 4940 2123 mt 4890 2173 L 5336 2263 mt 5386 2313 L 5386 2263 mt 5336 2313 L 5783 2307 mt 5833 2357 L 5833 2307 mt 5783 2357 L 6229 2350 mt 6279 2400 L 6279 2350 mt 6229 2400 L gs 898 388 5357 4226 MR c np DA 446 43 447 44 446 140 446 116 447 25 446 121 446 149 447 138 446 35 446 8 447 154 446 322 898 1080 13 MP stroke gr DA 1964 5154 mt (# of exactly treated findings) s 359 3350 mt -90 rotate (log-likelihood) s 90 rotate SO end eplot epage end showpage %%EndDocument endTexFig 75 1854 a Fm(Figure)g(2:)23 b(The)17 b(upp)q(er)h(b)q(ound)f(on)g(the) 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a(T)l(able)c(1:)k(Description)c(of)f (the)g(cases)g(for)g(whic)o(h)h(w)o(e)f(ev)m(aluated)h(the)f(exact)g(p) q(osterior)h(marginals.)204 1156 y(\(a\))277 631 y 10360626 8288501 2433925 12169625 36048404 39008583 startTexFig 277 631 a %%BeginDocument: figures/b-8.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 236 217 6127 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1909 4849 mt (1) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2980 4849 mt (2) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4052 4849 mt (3) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5123 4849 mt (4) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6194 4849 mt (5) s 898 4100 mt 952 4100 L 6254 4100 mt 6200 4100 L 497 4180 mt (-70) s 898 3364 mt 952 3364 L 6254 3364 mt 6200 3364 L 497 3444 mt (-60) s 898 2628 mt 952 2628 L 6254 2628 mt 6200 2628 L 497 2708 mt (-50) s 898 1892 mt 952 1892 L 6254 1892 mt 6200 1892 L 497 1972 mt (-40) s 898 1156 mt 952 1156 L 6254 1156 mt 6200 1156 L 497 1236 mt (-30) s 898 420 mt 952 420 L 6254 420 mt 6200 420 L 497 500 mt (-20) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np DA 1071 -735 1072 -257 1071 -2474 1969 4245 4 MP stroke 1071 -663 1072 -235 1071 -2178 1969 3837 4 MP stroke 1071 -585 1072 -198 1071 -1707 1969 3246 4 MP stroke SO gs 1896 706 3361 3613 MR c np 1933 4245 mt 2005 4245 L 1969 4209 mt 1969 4281 L 3004 1771 mt 3076 1771 L 3040 1735 mt 3040 1807 L 4076 1514 mt 4148 1514 L 4112 1478 mt 4112 1550 L 5147 779 mt 5219 779 L 5183 743 mt 5183 815 L gr gs 1896 688 3361 3223 MR c np 1933 3837 mt 2005 3837 L 1969 3801 mt 1969 3873 L 3004 1659 mt 3076 1659 L 3040 1623 mt 3040 1695 L 4076 1424 mt 4148 1424 L 4112 1388 mt 4112 1460 L 5147 761 mt 5219 761 L 5183 725 mt 5183 797 L gr gs 1896 683 3361 2637 MR c np 1933 3246 mt 2005 3246 L 1969 3210 mt 1969 3282 L 3004 1539 mt 3076 1539 L 3040 1503 mt 3040 1575 L 4076 1341 mt 4148 1341 L 4112 1305 mt 4112 1377 L 5147 756 mt 5219 756 L 5183 720 mt 5183 792 L gr gr 2963 5063 mt (sorted cases) s 442 3157 mt -90 rotate (log-likelihood) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 1014 1156 a Fm(\(b\))1090 631 y 10360626 8288501 2433925 12169625 36048404 39008583 startTexFig 1090 631 a %%BeginDocument: figures/b-12.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 236 217 6127 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1909 4849 mt (1) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2980 4849 mt (2) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 4052 4849 mt (3) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5123 4849 mt (4) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6194 4849 mt (5) s 898 4385 mt 952 4385 L 6254 4385 mt 6200 4385 L 497 4465 mt (-70) s 898 3591 mt 952 3591 L 6254 3591 mt 6200 3591 L 497 3671 mt (-60) s 898 2798 mt 952 2798 L 6254 2798 mt 6200 2798 L 497 2878 mt (-50) s 898 2004 mt 952 2004 L 6254 2004 mt 6200 2004 L 497 2084 mt (-40) s 898 1210 mt 952 1210 L 6254 1210 mt 6200 1210 L 497 1290 mt (-30) s 898 417 mt 952 417 L 6254 417 mt 6200 417 L 497 497 mt (-20) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np DA 1071 -804 1072 -266 1071 -2361 1969 4216 4 MP stroke 1071 -715 1072 -253 1071 -2349 1969 4102 4 MP stroke 1071 -667 1072 -236 1071 -2253 1969 3941 4 MP stroke SO gs 1896 712 3361 3578 MR c np 1933 4216 mt 2005 4216 L 1969 4180 mt 1969 4252 L 3004 1855 mt 3076 1855 L 3040 1819 mt 3040 1891 L 4076 1589 mt 4148 1589 L 4112 1553 mt 4112 1625 L 5147 785 mt 5219 785 L 5183 749 mt 5183 821 L gr gs 1896 712 3361 3464 MR c np 1933 4102 mt 2005 4102 L 1969 4066 mt 1969 4138 L 3004 1753 mt 3076 1753 L 3040 1717 mt 3040 1789 L 4076 1500 mt 4148 1500 L 4112 1464 mt 4112 1536 L 5147 785 mt 5219 785 L 5183 749 mt 5183 821 L gr gs 1896 712 3361 3303 MR c np 1933 3941 mt 2005 3941 L 1969 3905 mt 1969 3977 L 3004 1688 mt 3076 1688 L 3040 1652 mt 3040 1724 L 4076 1452 mt 4148 1452 L 4112 1416 mt 4112 1488 L 5147 785 mt 5219 785 L 5183 749 mt 5183 821 L gr gr 2963 5063 mt (sorted cases) s 442 3157 mt -90 rotate (log-likelihood) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 1262 a Fm(Figure)f(3:)23 b(Exact)j(v)m(alues)i(and)f(v)m (ariational)g(upp)q(er)h(and)f(lo)o(w)o(er)g(b)q(ounds)g(on)g(the)g (log-lik)o(eliho)q(o)q(d)277 1318 y(log)8 b Fi(P)e Fm(\()p Fi(f)423 1302 y Ft(+)453 1318 y Fg(j)p Fi(\030)r Fm(\))20 b(for)g(the)h(four)g(tractable)g(CPC)f(cases.)38 b(In)21 b(\(a\))f(8)h(p)q(ositiv)o(e)h(\014ndings)g(w)o(ere)277 1375 y(treated)14 b(exactly)l(,)i(and)f(in)h(\(b\))f(12)f(p)q(ositiv)o (e)j(\014ndings)f(w)o(ere)f(treated)g(exactly)l(.)75 1563 y(simply)i(means)f(that)g(the)g(\014nding)h(is)f(not)g (transformed)f(v)m(ariationally\).)24 b(In)16 b(panel)h(\(a\))e(there)i (w)o(ere)e(8)75 1620 y(p)q(ositiv)o(e)k(\014ndings)g(treated)e(exactly) l(,)i(and)f(in)h(\(b\))e(12)h(p)q(ositiv)o(e)g(\014ndings)i(w)o(ere)d (treated)h(exactly)l(.)28 b(As)75 1676 y(exp)q(ected,)16 b(the)f(b)q(ounds)h(w)o(ere)f(tigh)o(ter)g(when)h(more)f(p)q(ositiv)o (e)h(\014ndings)g(w)o(ere)f(treated)g(exactly)l(.)1748 1660 y Ft(4)146 1733 y Fm(The)21 b(a)o(v)o(erage)e(running)j(time)f (across)f(the)h(four)f(tractable)h(CPC)f(cases)h(w)o(as)f(26.9)f (seconds)j(for)75 1789 y(the)16 b(exact)f(metho)q(d,)g(0.11)f(seconds)i (for)f(the)g(v)m(ariational)i(metho)q(d)e(with)h(8)f(p)q(ositiv)o(e)i (\014ndings)f(treated)75 1845 y(exactly)l(,)11 b(and)g(0.85)e(seconds)i (for)f(the)g(v)m(ariational)h(metho)q(d)g(with)f(12)g(p)q(ositiv)o(e)h (\014ndings)h(treated)e(exactly)l(.)75 1902 y(\(These)15 b(results)h(w)o(ere)f(obtained)h(on)f(a)g(433)f(MHz)h(DEC)g(Alpha)h (computer\).)146 1958 y(Although)e(the)h(lik)o(eliho)q(o)q(d)i(is)d(an) g(imp)q(ortan)o(t)g(quan)o(tit)o(y)g(to)g(appro)o(ximate)f (\(particularly)i(in)g(appli-)75 2015 y(cations)e(in)g(whic)o(h)g (parameters)f(need)i(to)e(b)q(e)h(estimated\),)f(of)g(more)h(in)o (terest)f(in)i(the)e(QMR-DT)h(setting)75 2071 y(are)i(the)h(p)q (osterior)g(marginal)g(probabilities)i(for)d(the)h(individual)j (diseases.)j(As)16 b(w)o(e)f(discussed)i(in)g(the)75 2128 y(previous)i(section,)h(the)f(simplest)h(approac)o(h)e(to)g (obtaining)h(v)m(ariational)h(estimates)f(of)f(these)h(quan-)75 2184 y(tities)f(is)g(to)e(de\014ne)j(an)e(appro)o(ximate)f(v)m (ariational)j(distribution)f(based)g(either)g(on)f(the)g(distribution) 75 2241 y Fi(P)6 b Fm(\()p Fi(f)155 2224 y Ft(+)185 2241 y Fg(j)p Fi(\030)r Fm(\),)22 b(whic)o(h)h(upp)q(er-b)q(ounds)h(the)e (lik)o(eliho)q(o)q(d,)27 b(or)21 b(the)h(distribution)i Fi(P)6 b Fm(\()p Fi(f)1501 2224 y Ft(+)1531 2241 y Fg(j)p Fi(q)r Fm(\),)22 b(whic)o(h)h(lo)o(w)o(er-)75 2297 y(b)q(ounds)d(the)f (lik)o(eliho)q(o)q(d.)35 b(F)l(or)18 b(\014xed)i(v)m(alues)g(of)f(the)g (v)m(ariational)i(parameters)d(\(c)o(hosen)h(to)f(pro)o(vide)75 2354 y(a)h(tigh)o(t)h(b)q(ound)g(to)f(the)h(lik)o(eliho)q(o)q(d\),)j(b) q(oth)d(distributions)h(pro)o(vide)f(partially)h(factorized)f(appro)o (xi-)75 2410 y(mations)e(to)g(the)g(join)o(t)g(probabilit)o(y)i (distribution.)31 b(These)18 b(factorized)h(forms)e(can)i(b)q(e)g (exploited)g(as)p 75 2449 720 2 v 90 2492 a Fk(4.)e(Giv)o(en)11 b(that)f(a)f(signi\014can)o(t)k(fraction)d(of)f(the)h(p)q(ositiv)o(e)i (\014ndings)g(are)d(b)q(eing)i(treated)f(exactly)h(in)f(these)g(sim)o (ulation)q(s,)i(one)137 2537 y(ma)o(y)i(w)o(onder)f(what)h(if)f(an)o(y) h(additional)j(accuracy)d(is)g(due)g(to)f(the)g(v)n(ariational)k (transformations.)i(W)m(e)14 b(address)g(this)137 2583 y(concern)f(later)f(in)g(this)g(section)h(and)f(demonstrate)g(that)g (the)f(v)n(ariational)k(transformations)e(are)f(in)g(fact)f(resp)q (onsible)137 2629 y(for)i(a)g(signi\014can)o(t)j(p)q(ortion)e(of)f(the) g(accuracy)h(in)g(these)f(cases.)954 2753 y Fn(14)p eop %%Page: 15 15 15 14 bop 431 -100 a Fq(V)-5 b(aria)m(tional)17 b(Pr)o(obabilistic)e (Inference)h(and)h(QMR-DT)75 124 y Fm(e\016cien)o(t)e(appro)o(ximate)f (inference)i(engines)g(for)e(general)h(p)q(osterior)f(probabilities,)i (and)f(in)g(particular)75 181 y(w)o(e)c(can)h(use)g(them)f(to)g(pro)o (vide)h(appro)o(ximations)f(to)g(the)h(p)q(osterior)f(marginals)h(of)f (individual)k(diseases.)146 250 y(In)22 b(practice)h(w)o(e)f(found)h (that)e(the)i(distribution)h Fi(P)6 b Fm(\()p Fi(f)1123 234 y Ft(+)1152 250 y Fg(j)p Fi(\030)r Fm(\))22 b(yielded)i(more)e (accurate)g(p)q(osterior)75 307 y(marginals)14 b(than)g(the)g (distribution)i Fi(P)6 b Fm(\()p Fi(f)790 290 y Ft(+)820 307 y Fg(j)p Fi(q)r Fm(\),)13 b(and)h(w)o(e)g(restrict)g(our)g(presen)o (tation)g(to)f Fi(P)6 b Fm(\()p Fi(f)1680 290 y Ft(+)1710 307 y Fg(j)p Fi(\030)r Fm(\).)19 b(Fig-)75 363 y(ure)c(4)f(displa)o(ys) i(a)e(scatterplot)g(of)g(these)h(appro)o(ximate)f(p)q(osterior)g (marginals,)h(with)g(panel)h(\(a\))d(corre-)209 975 y(\(a\))283 450 y 10277741 8288501 2828615 12169625 36114186 39008583 startTexFig 283 450 a %%BeginDocument: figures/8-corr.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 302 217 6075 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1819 4849 mt (0.2) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2890 4849 mt (0.4) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3962 4849 mt (0.6) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5033 4849 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6194 4849 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 563 3848 mt (0.2) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 563 3003 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np gr gs 858 316 5471 4351 MR c np 36 36 6044 555 FO 36 36 5391 2530 FO 36 36 4031 1734 FO 36 36 3650 3068 FO 36 36 3626 2539 FO 36 36 3333 2674 FO 36 36 2183 3477 FO 36 36 2182 3576 FO 36 36 2140 4154 FO 36 36 2120 4259 FO 36 36 1845 3897 FO 36 36 1824 4094 FO 36 36 1764 2476 FO 36 36 1624 4364 FO 36 36 1594 4121 FO 36 36 1526 3921 FO 36 36 1515 4432 FO 36 36 1499 4280 FO 36 36 1494 4140 FO 36 36 1265 4336 FO 36 36 1254 4327 FO 36 36 1160 4118 FO 36 36 1141 4415 FO 36 36 1137 4543 FO 36 36 1102 4435 FO 36 36 1060 4484 FO 36 36 1025 4509 FO 36 36 1011 4559 FO 36 36 1003 4522 FO 36 36 1001 4529 FO 36 36 994 4558 FO 36 36 991 4537 FO 36 36 990 4538 FO 36 36 985 4572 FO 36 36 982 4541 FO 36 36 969 4555 FO 36 36 967 4593 FO 36 36 966 4587 FO 36 36 957 4564 FO 36 36 949 4561 FO 36 36 940 4578 FO 36 36 940 4579 FO 36 36 935 4579 FO 36 36 934 4583 FO 36 36 933 4585 FO 36 36 933 4584 FO 36 36 931 4587 FO 36 36 5458 1010 FO 36 36 3325 2726 FO 36 36 2724 3203 FO 36 36 2608 3281 FO 36 36 1803 3907 FO 36 36 1572 4095 FO 36 36 1335 4266 FO 36 36 1268 4313 FO 36 36 1222 4358 FO 36 36 1175 4396 FO 36 36 1138 4428 FO 36 36 1121 4439 FO 36 36 1106 4451 FO 36 36 1065 4480 FO 36 36 1059 4488 FO 36 36 1059 4485 FO 36 36 1057 4489 FO 36 36 1047 4496 FO 36 36 1047 4498 FO 36 36 1039 4498 FO 36 36 1038 4497 FO 36 36 1038 4503 FO 36 36 1034 4505 FO 36 36 1031 4510 FO 36 36 1023 4515 FO 36 36 1022 4513 FO 36 36 1019 4517 FO 36 36 1013 4524 FO 36 36 1012 4525 FO 36 36 1008 4527 FO 36 36 1007 4528 FO 36 36 1003 4531 FO 36 36 1002 4532 FO 36 36 1000 4534 FO 36 36 999 4535 FO 36 36 994 4538 FO 36 36 986 4542 FO 36 36 985 4546 FO 36 36 982 4547 FO 36 36 980 4550 FO 36 36 978 4550 FO 36 36 977 4551 FO 36 36 977 4552 FO 36 36 973 4554 FO 36 36 971 4556 FO 36 36 966 4559 FO 36 36 964 4562 FO 36 36 964 4562 FO 36 36 963 4562 FO 36 36 957 4566 FO 36 36 5447 1358 FO 36 36 4365 2052 FO 36 36 3991 3059 FO 36 36 2678 3538 FO 36 36 2634 3326 FO 36 36 2292 3951 FO 36 36 1840 3946 FO 36 36 1424 4345 FO 36 36 1371 3968 FO 36 36 1344 4152 FO 36 36 1256 4263 FO 36 36 1199 4409 FO 36 36 1152 3918 FO 36 36 1144 4464 FO 36 36 1124 4398 FO 36 36 1092 4533 FO 36 36 1067 4501 FO 36 36 1059 4483 FO 36 36 1034 4503 FO 36 36 1029 4499 FO 36 36 1009 4524 FO 36 36 1008 4539 FO 36 36 1002 4531 FO 36 36 997 4533 FO 36 36 991 4551 FO 36 36 986 4539 FO 36 36 982 4547 FO 36 36 981 4545 FO 36 36 973 4562 FO 36 36 971 4281 FO 36 36 970 4547 FO 36 36 969 4554 FO 36 36 969 4549 FO 36 36 968 4571 FO 36 36 968 4539 FO 36 36 967 4558 FO 36 36 967 4574 FO 36 36 963 4573 FO 36 36 957 4572 FO 36 36 955 4562 FO 36 36 953 4579 FO 36 36 945 4577 FO 36 36 944 4576 FO 36 36 944 4576 FO 36 36 940 4588 FO 36 36 939 4575 FO 36 36 936 4582 FO 36 36 936 4583 FO 36 36 936 4582 FO 36 36 934 4585 FO 36 36 6255 389 FO 36 36 4618 1518 FO 36 36 3619 2548 FO 36 36 2468 3465 FO 36 36 2238 3822 FO 36 36 1583 3924 FO 36 36 1483 4130 FO 36 36 1440 4203 FO 36 36 1254 4322 FO 36 36 1213 4374 FO 36 36 1212 4352 FO 36 36 1172 4398 FO 36 36 1138 4429 FO 36 36 1135 4488 FO 36 36 1132 4432 FO 36 36 1107 4451 FO 36 36 1096 4452 FO 36 36 1094 4463 FO 36 36 1085 4422 FO 36 36 1084 4450 FO 36 36 1082 4487 FO 36 36 1069 4421 FO 36 36 1043 4491 FO 36 36 1037 4505 FO 36 36 1020 4521 FO 36 36 1015 4495 FO 36 36 1014 4513 FO 36 36 1014 4524 FO 36 36 1012 4522 FO 36 36 1011 4523 FO 36 36 1009 4531 FO 36 36 1009 4529 FO 36 36 988 4542 FO 36 36 985 4549 FO 36 36 984 4541 FO 36 36 971 4550 FO 36 36 963 4563 FO 36 36 957 4567 FO 36 36 957 4566 FO 36 36 956 4574 FO 36 36 956 4569 FO 36 36 953 4571 FO 36 36 953 4563 FO 36 36 953 4571 FO 36 36 951 4572 FO 36 36 951 4575 FO 36 36 950 4528 FO 36 36 949 4580 FO 36 36 947 4554 FO 36 36 947 4575 FO gs 898 388 5357 4226 MR c np DO 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 54 -42 53 -43 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 54 -42 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 952 4571 100 MP stroke 54 -42 898 4613 2 MP stroke gr gr DO 2821 5063 mt (exact marginals) s 508 3483 mt -90 rotate (variational estimates) s 90 rotate SO end eplot epage end showpage %%EndDocument endTexFig 1014 975 a Fm(\(b\))1090 450 y 10277741 8288501 2828615 12169625 36114186 39008583 startTexFig 1090 450 a %%BeginDocument: figures/12-corr.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 302 217 6075 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1819 4849 mt (0.2) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2890 4849 mt (0.4) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3962 4849 mt (0.6) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5033 4849 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6194 4849 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 563 3848 mt (0.2) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 563 3003 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np gr gs 858 315 5471 4352 MR c np 36 36 6044 553 FO 36 36 5391 811 FO 36 36 4031 1755 FO 36 36 3650 2432 FO 36 36 3626 2410 FO 36 36 3333 2705 FO 36 36 2183 3698 FO 36 36 2182 4026 FO 36 36 2140 3772 FO 36 36 2120 4260 FO 36 36 1845 3831 FO 36 36 1824 4107 FO 36 36 1764 4186 FO 36 36 1624 4017 FO 36 36 1594 4086 FO 36 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4503 FO 36 36 1034 4506 FO 36 36 1031 4508 FO 36 36 1023 4515 FO 36 36 1022 4515 FO 36 36 1019 4518 FO 36 36 1013 4523 FO 36 36 1012 4523 FO 36 36 1008 4526 FO 36 36 1007 4527 FO 36 36 1003 4530 FO 36 36 1002 4531 FO 36 36 1000 4533 FO 36 36 999 4533 FO 36 36 994 4537 FO 36 36 986 4543 FO 36 36 985 4545 FO 36 36 982 4547 FO 36 36 980 4548 FO 36 36 978 4550 FO 36 36 977 4550 FO 36 36 977 4551 FO 36 36 973 4553 FO 36 36 971 4555 FO 36 36 966 4560 FO 36 36 964 4561 FO 36 36 964 4561 FO 36 36 963 4562 FO 36 36 957 4567 FO 36 36 5447 1401 FO 36 36 4365 1900 FO 36 36 3991 3054 FO 36 36 2678 3225 FO 36 36 2634 3242 FO 36 36 2292 3790 FO 36 36 1840 3791 FO 36 36 1424 4247 FO 36 36 1371 4154 FO 36 36 1344 4256 FO 36 36 1256 4317 FO 36 36 1199 4429 FO 36 36 1152 3985 FO 36 36 1144 4471 FO 36 36 1124 4387 FO 36 36 1092 4506 FO 36 36 1067 4510 FO 36 36 1059 4484 FO 36 36 1034 4504 FO 36 36 1029 4509 FO 36 36 1009 4524 FO 36 36 1008 4546 FO 36 36 1002 4531 FO 36 36 997 4534 FO 36 36 991 4556 FO 36 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36 1011 4524 FO 36 36 1009 4534 FO 36 36 1009 4532 FO 36 36 988 4554 FO 36 36 985 4551 FO 36 36 984 4543 FO 36 36 971 4550 FO 36 36 963 4563 FO 36 36 957 4568 FO 36 36 957 4559 FO 36 36 956 4572 FO 36 36 956 4570 FO 36 36 953 4572 FO 36 36 953 4572 FO 36 36 953 4573 FO 36 36 951 4572 FO 36 36 951 4566 FO 36 36 950 4573 FO 36 36 949 4583 FO 36 36 947 4567 FO 36 36 947 4575 FO gs 898 388 5357 4226 MR c np DO 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 54 -42 53 -43 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 54 -42 53 -42 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 54 -42 54 -42 53 -43 54 -42 53 -42 54 -42 53 -43 54 -42 54 -42 53 -42 54 -43 53 -42 54 -42 53 -42 54 -43 53 -42 952 4571 100 MP stroke 54 -42 898 4613 2 MP stroke gr gr DO 2821 5063 mt (exact marginals) s 508 3483 mt -90 rotate (variational estimates) s 90 rotate SO end eplot epage end showpage %%EndDocument endTexFig 75 1081 a Fm(Figure)i(4:)23 b(Scatterplot)d(of)g(the)g(v)m(ariational) i(p)q(osterior)e(estimates)g(and)h(the)f(exact)h(marginals.)35 b(In)277 1138 y(\(a\))16 b(8)h(p)q(ositiv)o(e)h(\014ndings)g(w)o(ere)f (treated)g(exactly)h(and)f(in)h(\(b\))f(12)g(p)q(ositiv)o(e)h (\014ndings)g(w)o(ere)277 1194 y(treated)c(exactly)l(.)75 1374 y(sp)q(onding)g(to)d(the)i(case)f(in)h(whic)o(h)h(8)e(p)q(ositiv)o (e)h(\014ndings)h(w)o(ere)e(treated)g(exactly)h(and)f(panel)i(\(b\))d (the)i(case)75 1430 y(in)19 b(whic)o(h)f(12)f(p)q(ositiv)o(e)i (\014ndings)g(treated)e(exactly)l(.)28 b(The)18 b(plots)f(w)o(ere)h (obtained)g(b)o(y)g(\014rst)f(extracting)75 1487 y(the)c(50)g(highest)h 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y(sampling)c(algorithm)g(roughly)g(co)o(v)o(ered)f(the)g (range)h(ac)o(hiev)o(ed)g(b)o(y)f(the)h(v)m(ariational)g(algorithm.)24 b(The)75 929 y(results)12 b(are)f(sho)o(wn)h(in)g(Figure)g(5,)g(with)g (the)f(righ)o(t-hand)h(curv)o(e)g(corresp)q(onding)h(to)e(the)h (sampling)g(runs.)75 985 y(The)21 b(\014gure)g(displa)o(ys)h(the)f (mean)g(correlations)g(b)q(et)o(w)o(een)g(the)g(appro)o(ximate)f(and)h (exact)g(p)q(osterior)75 1042 y(marginals)15 b(across)e(ten)i(indep)q (enden)o(t)i(runs)d(of)g(the)h(algorithm)f(\(for)g(the)g(four)g (tractable)h(CPC)f(cases\).)582 1117 y 11637034 9235744 2105016 11840716 36508876 39008583 startTexFig 582 1117 a %%BeginDocument: figures/corr.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0204 7344 csm 182 217 6281 4962 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w 0 4224 5356 0 0 -4224 898 4612 4 MP PP -5356 0 0 4224 5356 0 0 -4224 898 4612 5 MP stroke 4 w DO SO 6 w 0 sg 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L 898 4612 mt 6254 4612 L 898 4612 mt 898 388 L 898 4612 mt 898 4558 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 696 4915 mt (10) s /Helvetica /ISOLatin1Encoding 144 FMSR 936 4781 mt (-1) s 2683 4612 mt 2683 4558 L 2683 388 mt 2683 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 2523 4915 mt (10) s /Helvetica /ISOLatin1Encoding 144 FMSR 2763 4781 mt (0) s 4469 4612 mt 4469 4558 L 4469 388 mt 4469 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 4309 4915 mt (10) s /Helvetica /ISOLatin1Encoding 144 FMSR 4549 4781 mt (1) s 6254 4612 mt 6254 4558 L 6254 388 mt 6254 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 6094 4915 mt (10) s /Helvetica /ISOLatin1Encoding 144 FMSR 6334 4781 mt (2) s 898 4612 mt 952 4612 L 6254 4612 mt 6200 4612 L /Helvetica /ISOLatin1Encoding 216 FMSR 443 4692 mt (0.86) s 898 4009 mt 952 4009 L 6254 4009 mt 6200 4009 L 443 4089 mt (0.88) s 898 3405 mt 952 3405 L 6254 3405 mt 6200 3405 L 563 3485 mt (0.9) s 898 2802 mt 952 2802 L 6254 2802 mt 6200 2802 L 443 2882 mt (0.92) s 898 2198 mt 952 2198 L 6254 2198 mt 6200 2198 L 443 2278 mt (0.94) s 898 1595 mt 952 1595 L 6254 1595 mt 6200 1595 L 443 1675 mt (0.96) s 898 991 mt 952 991 L 6254 991 mt 6200 991 L 443 1071 mt (0.98) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L gs 898 388 5357 4225 MR c np 1022 -177 1566 -528 989 1165 3 MP stroke gr gs 916 387 2735 852 MR c np 36 36 989 1165 FO 36 36 2555 637 FO 36 36 3577 460 FO gr gs 898 388 5357 4225 MR c np DA 513 -381 525 -1317 567 -404 4092 2620 4 MP stroke SO gs 4019 445 1752 2249 MR c np 0 j -41 71 -41 -71 82 0 4051 2644 4 MP DP -41 71 -41 -71 82 0 4618 2240 4 MP DP -41 71 -41 -71 82 0 5143 923 4 MP DP -41 71 -41 -71 82 0 5656 542 4 MP DP gr DO 513 -1192 525 -2305 567 -182 4092 4291 4 MP stroke SO gs 4019 539 1752 3826 MR c np 4056 4291 mt 4128 4291 L 4092 4255 mt 4092 4327 L 4623 4109 mt 4695 4109 L 4659 4073 mt 4659 4145 L 5148 1804 mt 5220 1804 L 5184 1768 mt 5184 1840 L 5661 612 mt 5733 612 L 5697 576 mt 5697 648 L gr DO 513 -61 525 -446 567 -232 4092 1193 4 MP stroke SO gr gs 4019 381 1752 886 MR c np 4056 1193 mt 4128 1193 L 4092 1157 mt 4092 1229 L 4623 961 mt 4695 961 L 4659 925 mt 4659 997 L 5148 515 mt 5220 515 L 5184 479 mt 5184 551 L 5661 454 mt 5733 454 L 5697 418 mt 5697 490 L gr gs 898 388 5357 4225 MR c np gr 2335 5129 mt (execution time in seconds) s 388 3303 mt -90 rotate (mean correlation) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 1808 a Fm(Figure)h(5:)23 b(The)14 b(mean)h(correlation)f(b)q(et)o 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b(\(the)f(left-hand)h(curv)o(e\).)19 b(The)12 b(three)f(p)q(oin)o(ts)h(on)g(the)g(curv)o(e)f(corresp)q(ond)h (to)f(up)h(to)f(8,)h(12)f(and)p 75 2449 720 2 v 90 2492 a Fk(5.)17 b(The)c(initiali)q(zati)q(on)j(metho)q(d)e(pro)o(v)o(ed)g (to)f(ha)o(v)o(e)g(little)i(e\013ect)e(on)h(the)f(inference)h(results.) 90 2537 y(6.)j(W)m(e)d(also)h(in)o(v)o(estigated)h(Gibbs)f(sampling)h (\(P)o(earl,)f(1988\).)k(The)14 b(results)h(from)e(Gibbs)j(sampling)g (w)o(ere)d(not)h(as)g(go)q(o)q(d)137 2583 y(as)f(the)g(results)i(from)d (lik)o(eliho)r(o)q(d-w)o(ei)q(gh)o(ted)k(sampling,)f(and)f(w)o(e)e(rep) q(ort)i(only)g(the)f(latter)g(results)h(in)g(the)f(remainder)137 2629 y(of)g(the)g(pap)q(er.)954 2753 y Fn(16)p eop %%Page: 17 17 17 16 bop 431 -100 a Fq(V)-5 b(aria)m(tional)17 b(Pr)o(obabilistic)e (Inference)h(and)h(QMR-DT)75 124 y Fm(16)g(p)q(ositiv)o(e)h(\014ndings) h(treated)e(exactly)l(.)26 b(Note)17 b(that)g(the)h(v)m(ariational)g (estimates)f(are)g(deterministic)75 181 y(and)e(th)o(us)g(only)h(a)f 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b(false)g(p)q(ositiv)o(es)g(as)f(a)g(function)i(of)e(true)g(p)q(ositiv) o(es)75 976 y(pro)o(vides)k(a)f(meaningful)i(and)f(useful)g(measure)g (of)f(the)g(accuracy)h(of)f(an)h(appro)o(ximation)f(sc)o(heme.)75 1033 y(T)l(o)e(the)h(exten)o(t)f(that)g(a)g(metho)q(d)h(pro)o(vides)g (a)g(nearly)g(correct)f(ranking)h(of)f(true)h(p)q(ositiv)o(es)g(the)g (plot)75 1089 y(increases)d(slo)o(wly)g(and)g(the)g(area)f(under)h(the) f(curv)o(e)h(is)g(small.)22 b(When)16 b(a)f(signi\014can)o(t)h(disease) h(app)q(ears)75 1146 y(late)d(in)h(the)e(appro)o(ximate)h(ordering)g (the)g(plot)g(increases)g(rapidly)h(near)f(the)g(true)f(rank)h(of)f (the)h(missed)75 1202 y(disease)i(and)f(the)h(area)e(under)i(the)f (curv)o(e)h(is)g(large.)146 1261 y(W)l(e)g(also)h(plot)f(the)h(n)o(um)o (b)q(er)g(of)f(\\false)g(negativ)o(es")g(in)i(a)e(set)g(of)g(top)g Fi(N)21 b Fm(highly)d(rank)o(ed)f(diseases.)75 1318 y(F)l(alse)22 b(negativ)o(es)g(refer)f(to)g(the)h(n)o(um)o(b)q(er)g(of)f(diseases,)j (out)d(of)g(the)h Fi(N)k Fm(highest)d(ranking)f(diseases,)75 1374 y(that)c(do)g(not)g(app)q(ear)h(in)g(the)g(set)f(of)g Fi(N)23 b Fm(appro)o(ximately)18 b(rank)o(ed)h(diseases.)30 b(Note)18 b(that)g(unlik)o(e)i(the)75 1431 y(previous)13 b(measure,)g(this)g(measure)f(do)q(es)h(not)f(rev)o(eal)g(the)h(sev)o (erit)o(y)f(of)g(the)h(misplacemen)o(ts,)g(only)g(their)75 1487 y(frequency)l(.)146 1546 y(With)k(this)g(impro)o(v)o(ed)g (diagnostic)g(measure)g(in)h(hand,)f(let)h(us)e(return)h(to)f(the)h(ev) m(aluation)h(of)f(the)75 1603 y(inference)g(algorithms,)f(b)q(eginning) h(with)f(the)g(v)m(ariational)h(algorithm.)k(Figure)16 b(6)f(pro)o(vides)h(plots)g(of)220 2192 y(\(a\))293 1667 y 10194856 8288501 3157524 12169625 36377313 39008583 startTexFig 293 1667 a %%BeginDocument: figures/8-lo.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 362 217 6061 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1849 4849 mt (10) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2920 4849 mt (20) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3992 4849 mt (30) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5063 4849 mt (40) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6134 4849 mt (50) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 3909 mt 952 3909 L 6254 3909 mt 6200 3909 L 623 3989 mt (10) s 898 3205 mt 952 3205 L 6254 3205 mt 6200 3205 L 623 3285 mt (20) s 898 2501 mt 952 2501 L 6254 2501 mt 6200 2501 L 623 2581 mt (30) s 898 1796 mt 952 1796 L 6254 1796 mt 6200 1796 L 623 1876 mt (40) s 898 1092 mt 952 1092 L 6254 1092 mt 6200 1092 L 623 1172 mt (50) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 623 468 mt (60) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 107 53 107 70 107 0 107 18 108 35 107 -141 107 53 107 53 107 52 107 -35 107 -105 107 52 108 -387 107 -88 107 35 107 53 107 -158 107 17 107 53 107 0 108 53 107 -53 107 -70 107 52 107 71 107 -123 107 -194 107 35 107 0 108 71 107 52 107 36 107 52 107 18 107 -53 107 35 107 -193 108 0 107 0 107 53 107 0 107 -88 107 -71 107 18 107 -18 108 35 107 -52 107 17 107 -35 1005 4613 50 MP stroke gr gs 932 3625 5396 1062 MR c np 36 36 1005 4613 FO 36 36 1112 4578 FO 36 36 1219 4595 FO 36 36 1326 4543 FO 36 36 1434 4578 FO 36 36 1541 4560 FO 36 36 1648 4578 FO 36 36 1755 4507 FO 36 36 1862 4419 FO 36 36 1969 4419 FO 36 36 2076 4472 FO 36 36 2183 4472 FO 36 36 2291 4472 FO 36 36 2398 4279 FO 36 36 2505 4314 FO 36 36 2612 4261 FO 36 36 2719 4279 FO 36 36 2826 4331 FO 36 36 2933 4367 FO 36 36 3040 4419 FO 36 36 3148 4490 FO 36 36 3255 4490 FO 36 36 3362 4525 FO 36 36 3469 4331 FO 36 36 3576 4208 FO 36 36 3683 4279 FO 36 36 3790 4331 FO 36 36 3897 4261 FO 36 36 4004 4208 FO 36 36 4112 4261 FO 36 36 4219 4261 FO 36 36 4326 4314 FO 36 36 4433 4331 FO 36 36 4540 4173 FO 36 36 4647 4226 FO 36 36 4754 4261 FO 36 36 4861 4173 FO 36 36 4969 3786 FO 36 36 5076 3838 FO 36 36 5183 3733 FO 36 36 5290 3698 FO 36 36 5397 3750 FO 36 36 5504 3803 FO 36 36 5611 3856 FO 36 36 5718 3715 FO 36 36 5826 3750 FO 36 36 5933 3768 FO 36 36 6040 3768 FO 36 36 6147 3838 FO 36 36 6254 3891 FO gr gs 898 388 5357 4226 MR c np DA 107 17 107 53 107 -211 107 -18 108 36 107 -1391 107 70 107 -17 107 70 107 0 107 70 107 -140 108 35 107 -387 107 70 107 70 107 71 107 -176 107 -18 107 35 108 -35 107 71 107 70 107 70 107 -140 107 52 107 53 107 -211 107 0 108 53 107 17 107 -581 107 -17 107 53 107 35 107 35 107 -88 108 -405 107 0 107 -53 107 -17 107 -616 107 -18 107 53 107 -18 108 53 107 -581 107 18 107 -194 1005 4613 50 MP stroke SO gr gs 932 368 5396 4319 MR c np 980 4588 mt 1030 4638 L 1030 4588 mt 980 4638 L 1087 4394 mt 1137 4444 L 1137 4394 mt 1087 4444 L 1194 4412 mt 1244 4462 L 1244 4412 mt 1194 4462 L 1301 3831 mt 1351 3881 L 1351 3831 mt 1301 3881 L 1409 3884 mt 1459 3934 L 1459 3884 mt 1409 3934 L 1516 3866 mt 1566 3916 L 1566 3866 mt 1516 3916 L 1623 3919 mt 1673 3969 L 1673 3919 mt 1623 3969 L 1730 3901 mt 1780 3951 L 1780 3901 mt 1730 3951 L 1837 3285 mt 1887 3335 L 1887 3285 mt 1837 3335 L 1944 3268 mt 1994 3318 L 1994 3268 mt 1944 3318 L 2051 3215 mt 2101 3265 L 2101 3215 mt 2051 3265 L 2158 3215 mt 2208 3265 L 2208 3215 mt 2158 3265 L 2266 2810 mt 2316 2860 L 2316 2810 mt 2266 2860 L 2373 2722 mt 2423 2772 L 2423 2722 mt 2373 2772 L 2480 2757 mt 2530 2807 L 2530 2757 mt 2480 2807 L 2587 2792 mt 2637 2842 L 2637 2792 mt 2587 2842 L 2694 2845 mt 2744 2895 L 2744 2845 mt 2694 2895 L 2801 2828 mt 2851 2878 L 2851 2828 mt 2801 2878 L 2908 2247 mt 2958 2297 L 2958 2247 mt 2908 2297 L 3015 2264 mt 3065 2314 L 3065 2264 mt 3015 2314 L 3123 2317 mt 3173 2367 L 3173 2317 mt 3123 2367 L 3230 2317 mt 3280 2367 L 3280 2317 mt 3230 2367 L 3337 2106 mt 3387 2156 L 3387 2106 mt 3337 2156 L 3444 2159 mt 3494 2209 L 3494 2159 mt 3444 2209 L 3551 2211 mt 3601 2261 L 3601 2211 mt 3551 2261 L 3658 2071 mt 3708 2121 L 3708 2071 mt 3658 2121 L 3765 2141 mt 3815 2191 L 3815 2141 mt 3765 2191 L 3872 2211 mt 3922 2261 L 3922 2211 mt 3872 2261 L 3979 2282 mt 4029 2332 L 4029 2282 mt 3979 2332 L 4087 2247 mt 4137 2297 L 4137 2247 mt 4087 2297 L 4194 2282 mt 4244 2332 L 4244 2282 mt 4194 2332 L 4301 2264 mt 4351 2314 L 4351 2264 mt 4301 2314 L 4408 2088 mt 4458 2138 L 4458 2088 mt 4408 2138 L 4515 2159 mt 4565 2209 L 4565 2159 mt 4515 2209 L 4622 2229 mt 4672 2279 L 4672 2229 mt 4622 2279 L 4729 2299 mt 4779 2349 L 4779 2299 mt 4729 2349 L 4836 1912 mt 4886 1962 L 4886 1912 mt 4836 1962 L 4944 1947 mt 4994 1997 L 4994 1947 mt 4944 1997 L 5051 1807 mt 5101 1857 L 5101 1807 mt 5051 1857 L 5158 1877 mt 5208 1927 L 5208 1877 mt 5158 1927 L 5265 1877 mt 5315 1927 L 5315 1877 mt 5265 1927 L 5372 1947 mt 5422 1997 L 5422 1947 mt 5372 1997 L 5479 1930 mt 5529 1980 L 5529 1930 mt 5479 1980 L 5586 2000 mt 5636 2050 L 5636 2000 mt 5586 2050 L 5693 609 mt 5743 659 L 5743 609 mt 5693 659 L 5801 645 mt 5851 695 L 5851 645 mt 5801 695 L 5908 627 mt 5958 677 L 5958 627 mt 5908 677 L 6015 416 mt 6065 466 L 6065 416 mt 6015 466 L 6122 469 mt 6172 519 L 6172 469 mt 6122 519 L 6229 486 mt 6279 536 L 6279 486 mt 6229 536 L gr gs 898 388 5357 4226 MR c np gr 2910 5063 mt (true positives) s 568 3179 mt -90 rotate (false positives) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 1019 2192 a Fm(\(b\))1095 1667 y 10029086 8288501 3815342 12169625 36377313 39008583 startTexFig 1095 1667 a %%BeginDocument: figures/8-lo-fn.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 482 217 5941 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1849 4849 mt (10) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2920 4849 mt (20) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3992 4849 mt (30) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5063 4849 mt (40) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6134 4849 mt (50) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 4009 mt 952 4009 L 6254 4009 mt 6200 4009 L 743 4089 mt (1) s 898 3406 mt 952 3406 L 6254 3406 mt 6200 3406 L 743 3486 mt (2) s 898 2802 mt 952 2802 L 6254 2802 mt 6200 2802 L 743 2882 mt (3) s 898 2199 mt 952 2199 L 6254 2199 mt 6200 2199 L 743 2279 mt (4) s 898 1595 mt 952 1595 L 6254 1595 mt 6200 1595 L 743 1675 mt (5) s 898 992 mt 952 992 L 6254 992 mt 6200 992 L 743 1072 mt (6) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (7) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 107 -301 107 0 107 -151 107 -302 108 -151 107 -302 107 -302 107 0 107 -150 107 -151 107 -151 107 -151 108 -151 107 -302 107 151 107 151 107 -302 107 151 107 -302 107 -151 108 151 107 0 107 0 107 -151 107 151 107 -452 107 0 107 151 107 150 108 151 107 302 107 0 107 -151 107 -302 107 302 107 0 107 -452 108 0 107 -151 107 151 107 -302 107 0 107 0 107 0 107 -151 108 151 107 -151 107 0 107 -151 1005 4613 50 MP stroke gr gs 932 919 5396 3768 MR c np 36 36 1005 4613 FO 36 36 1112 4462 FO 36 36 1219 4462 FO 36 36 1326 4311 FO 36 36 1434 4462 FO 36 36 1541 4311 FO 36 36 1648 4311 FO 36 36 1755 4311 FO 36 36 1862 4311 FO 36 36 1969 4009 FO 36 36 2076 4160 FO 36 36 2183 4009 FO 36 36 2291 4009 FO 36 36 2398 3557 FO 36 36 2505 3557 FO 36 36 2612 3859 FO 36 36 2719 3557 FO 36 36 2826 3406 FO 36 36 2933 3406 FO 36 36 3040 3708 FO 36 36 3148 3859 FO 36 36 3255 4009 FO 36 36 3362 4160 FO 36 36 3469 4160 FO 36 36 3576 3708 FO 36 36 3683 3859 FO 36 36 3790 3708 FO 36 36 3897 3708 FO 36 36 4004 3708 FO 36 36 4112 3859 FO 36 36 4219 3708 FO 36 36 4326 3406 FO 36 36 4433 3557 FO 36 36 4540 3255 FO 36 36 4647 3406 FO 36 36 4754 3557 FO 36 36 4861 3255 FO 36 36 4969 3104 FO 36 36 5076 2953 FO 36 36 5183 2802 FO 36 36 5290 2651 FO 36 36 5397 2501 FO 36 36 5504 2501 FO 36 36 5611 2199 FO 36 36 5718 1897 FO 36 36 5826 1746 FO 36 36 5933 1444 FO 36 36 6040 1293 FO 36 36 6147 1293 FO 36 36 6254 992 FO gr gs 898 388 5357 4226 MR c np DA 107 -150 107 0 107 301 107 0 108 0 107 -151 107 0 107 151 107 -151 107 -301 107 151 107 -151 108 -453 107 -151 107 302 107 0 107 -302 107 0 107 -151 107 -151 108 151 107 302 107 -151 107 151 107 -302 107 -151 107 0 107 151 107 -151 108 -151 107 -151 107 -150 107 0 107 -302 107 0 107 0 107 -453 108 -151 107 0 107 0 107 -302 107 0 107 -150 107 150 107 -301 108 151 107 -151 107 -151 107 -302 1005 4613 50 MP stroke SO gr gs 932 768 5396 3919 MR c np 980 4588 mt 1030 4638 L 1030 4588 mt 980 4638 L 1087 4286 mt 1137 4336 L 1137 4286 mt 1087 4336 L 1194 4135 mt 1244 4185 L 1244 4135 mt 1194 4185 L 1301 3984 mt 1351 4034 L 1351 3984 mt 1301 4034 L 1409 4135 mt 1459 4185 L 1459 4135 mt 1409 4185 L 1516 3834 mt 1566 3884 L 1566 3834 mt 1516 3884 L 1623 3984 mt 1673 4034 L 1673 3984 mt 1623 4034 L 1730 3834 mt 1780 3884 L 1780 3834 mt 1730 3884 L 1837 3834 mt 1887 3884 L 1887 3834 mt 1837 3884 L 1944 3532 mt 1994 3582 L 1994 3532 mt 1944 3582 L 2051 3532 mt 2101 3582 L 2101 3532 mt 2051 3582 L 2158 3532 mt 2208 3582 L 2208 3532 mt 2158 3582 L 2266 3381 mt 2316 3431 L 2316 3381 mt 2266 3431 L 2373 2928 mt 2423 2978 L 2423 2928 mt 2373 2978 L 2480 2928 mt 2530 2978 L 2530 2928 mt 2480 2978 L 2587 2928 mt 2637 2978 L 2637 2928 mt 2587 2978 L 2694 2626 mt 2744 2676 L 2744 2626 mt 2694 2676 L 2801 2626 mt 2851 2676 L 2851 2626 mt 2801 2676 L 2908 2476 mt 2958 2526 L 2958 2476 mt 2908 2526 L 3015 2325 mt 3065 2375 L 3065 2325 mt 3015 2375 L 3123 2174 mt 3173 2224 L 3173 2174 mt 3123 2224 L 3230 2023 mt 3280 2073 L 3280 2023 mt 3230 2073 L 3337 2174 mt 3387 2224 L 3387 2174 mt 3337 2224 L 3444 2174 mt 3494 2224 L 3494 2174 mt 3444 2224 L 3551 2023 mt 3601 2073 L 3601 2023 mt 3551 2073 L 3658 1721 mt 3708 1771 L 3708 1721 mt 3658 1771 L 3765 1872 mt 3815 1922 L 3815 1872 mt 3765 1922 L 3872 1721 mt 3922 1771 L 3922 1721 mt 3872 1771 L 3979 2023 mt 4029 2073 L 4029 2023 mt 3979 2073 L 4087 2174 mt 4137 2224 L 4137 2174 mt 4087 2224 L 4194 2023 mt 4244 2073 L 4244 2023 mt 4194 2073 L 4301 1872 mt 4351 1922 L 4351 1872 mt 4301 1922 L 4408 1872 mt 4458 1922 L 4458 1872 mt 4408 1922 L 4515 1570 mt 4565 1620 L 4565 1570 mt 4515 1620 L 4622 1570 mt 4672 1620 L 4672 1570 mt 4622 1620 L 4729 1872 mt 4779 1922 L 4779 1872 mt 4729 1922 L 4836 1721 mt 4886 1771 L 4886 1721 mt 4836 1771 L 4944 1268 mt 4994 1318 L 4994 1268 mt 4944 1318 L 5051 1117 mt 5101 1167 L 5101 1117 mt 5051 1167 L 5158 1268 mt 5208 1318 L 5208 1268 mt 5158 1318 L 5265 967 mt 5315 1017 L 5315 967 mt 5265 1017 L 5372 816 mt 5422 866 L 5422 816 mt 5372 866 L 5479 967 mt 5529 1017 L 5529 967 mt 5479 1017 L 5586 967 mt 5636 1017 L 5636 967 mt 5586 1017 L 5693 816 mt 5743 866 L 5743 816 mt 5693 866 L 5801 816 mt 5851 866 L 5851 816 mt 5801 866 L 5908 816 mt 5958 866 L 5958 816 mt 5908 866 L 6015 1117 mt 6065 1167 L 6065 1117 mt 6015 1167 L 6122 1117 mt 6172 1167 L 6172 1117 mt 6122 1167 L 6229 967 mt 6279 1017 L 6279 967 mt 6229 1017 L gr gs 898 388 5357 4226 MR c np gr 2599 5063 mt (approximate ranking) s 688 3221 mt -90 rotate (false negatives) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 2298 a Fm(Figure)f(6:)23 b(\(a\))12 b(Av)o(erage)h(n)o(um)o(b)q(er) h(of)f(false)h(p)q(ositiv)o(es)h(as)e(a)g(function)i(of)e(true)g(p)q (ositiv)o(es)i(for)e(the)g(v)m(aria-)277 2354 y(tional)e(metho)q(d)h (\(solid)f(lines\))i(and)e(the)g(partially-exact)h(metho)q(d)g (\(dashed)f(line\).)20 b(\(b\))11 b(F)l(alse)277 2411 y(negativ)o(es)18 b(in)g(the)h(set)e(of)h(top)g Fi(N)k Fm(appro)o(ximately)c(rank)o(ed)g(diseases.)29 b(In)19 b(b)q(oth)f(\014gures)g(8)277 2467 y(p)q(ositiv)o(e)e(\014ndings)g(w)o (ere)f(treated)g(exactly)l(.)75 2629 y(the)h(false)f(p)q(ositiv)o(es)i (\(panel)f(a\))f(and)g(false)h(negativ)o(es)f(\(panel)i(b\))e(against)g (the)g(true)h(p)q(ositiv)o(es)g(for)f(the)954 2753 y Fn(17)p eop %%Page: 18 18 18 17 bop 759 -100 a Fq(Jaakk)o(ola)18 b(&)e(Jord)o(an)209 604 y Fm(\(a\))283 79 y 10194856 8288501 3157524 12169625 36377313 39008583 startTexFig 283 79 a %%BeginDocument: figures/12-lo.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 362 217 6061 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1849 4849 mt (10) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2920 4849 mt (20) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3992 4849 mt (30) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5063 4849 mt (40) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6134 4849 mt (50) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 4085 mt 952 4085 L 6254 4085 mt 6200 4085 L 743 4165 mt (5) s 898 3557 mt 952 3557 L 6254 3557 mt 6200 3557 L 623 3637 mt (10) s 898 3029 mt 952 3029 L 6254 3029 mt 6200 3029 L 623 3109 mt (15) s 898 2501 mt 952 2501 L 6254 2501 mt 6200 2501 L 623 2581 mt (20) s 898 1972 mt 952 1972 L 6254 1972 mt 6200 1972 L 623 2052 mt (25) s 898 1444 mt 952 1444 L 6254 1444 mt 6200 1444 L 623 1524 mt (30) s 898 916 mt 952 916 L 6254 916 mt 6200 916 L 623 996 mt (35) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 623 468 mt (40) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 107 -105 107 79 107 -238 107 -26 108 53 107 53 107 26 107 26 107 53 107 79 107 0 107 80 108 -634 107 -79 107 52 107 80 107 -27 107 -53 107 53 107 27 108 79 107 79 107 -106 107 80 107 79 107 -106 107 -158 107 -27 107 -158 108 0 107 79 107 79 107 0 107 -105 107 0 107 79 107 -79 108 53 107 -27 107 53 107 -132 107 26 107 -158 107 0 107 0 108 53 107 -53 107 0 107 0 1005 4613 50 MP stroke gr gs 932 3589 5396 1098 MR c np 36 36 1005 4613 FO 36 36 1112 4613 FO 36 36 1219 4613 FO 36 36 1326 4560 FO 36 36 1434 4613 FO 36 36 1541 4613 FO 36 36 1648 4613 FO 36 36 1755 4455 FO 36 36 1862 4481 FO 36 36 1969 4349 FO 36 36 2076 4402 FO 36 36 2183 4375 FO 36 36 2291 4428 FO 36 36 2398 4349 FO 36 36 2505 4428 FO 36 36 2612 4428 FO 36 36 2719 4323 FO 36 36 2826 4323 FO 36 36 2933 4402 FO 36 36 3040 4481 FO 36 36 3148 4481 FO 36 36 3255 4323 FO 36 36 3362 4296 FO 36 36 3469 4138 FO 36 36 3576 4032 FO 36 36 3683 4111 FO 36 36 3790 4191 FO 36 36 3897 4085 FO 36 36 4004 4164 FO 36 36 4112 4243 FO 36 36 4219 4270 FO 36 36 4326 4323 FO 36 36 4433 4270 FO 36 36 4540 4243 FO 36 36 4647 4323 FO 36 36 4754 4375 FO 36 36 4861 4296 FO 36 36 4969 3662 FO 36 36 5076 3742 FO 36 36 5183 3742 FO 36 36 5290 3821 FO 36 36 5397 3874 FO 36 36 5504 3900 FO 36 36 5611 3926 FO 36 36 5718 3979 FO 36 36 5826 4032 FO 36 36 5933 4006 FO 36 36 6040 3768 FO 36 36 6147 3847 FO 36 36 6254 3742 FO gr gs 898 388 5357 4226 MR c np DA 107 79 107 79 107 -554 107 79 108 79 107 79 107 80 107 79 107 79 107 79 107 79 107 -1452 108 -132 107 79 107 80 107 79 107 79 107 -264 107 79 107 79 108 -924 107 79 107 80 107 79 107 79 107 26 107 80 107 -291 107 -185 108 80 107 79 107 -53 107 79 107 79 107 -1056 107 -79 107 79 108 -238 107 -52 107 52 107 -52 107 -159 107 -105 107 79 107 -79 108 79 107 -132 107 -53 107 26 1005 4587 50 MP stroke SO gr gs 932 738 5396 3949 MR c np 980 4562 mt 1030 4612 L 1030 4562 mt 980 4612 L 1087 4588 mt 1137 4638 L 1137 4588 mt 1087 4638 L 1194 4535 mt 1244 4585 L 1244 4535 mt 1194 4585 L 1301 4403 mt 1351 4453 L 1351 4403 mt 1301 4453 L 1409 4482 mt 1459 4532 L 1459 4482 mt 1409 4532 L 1516 4403 mt 1566 4453 L 1566 4403 mt 1516 4453 L 1623 4482 mt 1673 4532 L 1673 4482 mt 1623 4532 L 1730 4377 mt 1780 4427 L 1780 4377 mt 1730 4427 L 1837 4218 mt 1887 4268 L 1887 4218 mt 1837 4268 L 1944 4166 mt 1994 4216 L 1994 4166 mt 1944 4216 L 2051 4218 mt 2101 4268 L 2101 4218 mt 2051 4268 L 2158 4166 mt 2208 4216 L 2208 4166 mt 2158 4216 L 2266 3928 mt 2316 3978 L 2316 3928 mt 2266 3978 L 2373 4007 mt 2423 4057 L 2423 4007 mt 2373 4057 L 2480 3928 mt 2530 3978 L 2530 3928 mt 2480 3978 L 2587 2872 mt 2637 2922 L 2637 2872 mt 2587 2922 L 2694 2951 mt 2744 3001 L 2744 2951 mt 2694 3001 L 2801 3030 mt 2851 3080 L 2851 3030 mt 2801 3080 L 2908 2977 mt 2958 3027 L 2958 2977 mt 2908 3027 L 3015 3056 mt 3065 3106 L 3065 3056 mt 3015 3106 L 3123 3136 mt 3173 3186 L 3173 3136 mt 3123 3186 L 3230 2951 mt 3280 3001 L 3280 2951 mt 3230 3001 L 3337 2660 mt 3387 2710 L 3387 2660 mt 3337 2710 L 3444 2740 mt 3494 2790 L 3494 2740 mt 3444 2790 L 3551 2766 mt 3601 2816 L 3601 2766 mt 3551 2816 L 3658 2845 mt 3708 2895 L 3708 2845 mt 3658 2895 L 3765 2924 mt 3815 2974 L 3815 2924 mt 3765 2974 L 3872 3004 mt 3922 3054 L 3922 3004 mt 3872 3054 L 3979 3083 mt 4029 3133 L 4029 3083 mt 3979 3133 L 4087 2159 mt 4137 2209 L 4137 2159 mt 4087 2209 L 4194 2238 mt 4244 2288 L 4244 2238 mt 4194 2288 L 4301 2317 mt 4351 2367 L 4351 2317 mt 4301 2367 L 4408 2053 mt 4458 2103 L 4458 2053 mt 4408 2103 L 4515 2132 mt 4565 2182 L 4565 2132 mt 4515 2182 L 4622 2211 mt 4672 2261 L 4672 2211 mt 4622 2261 L 4729 2291 mt 4779 2341 L 4779 2291 mt 4729 2341 L 4836 2370 mt 4886 2420 L 4886 2370 mt 4836 2420 L 4944 2238 mt 4994 2288 L 4994 2238 mt 4944 2288 L 5051 786 mt 5101 836 L 5101 786 mt 5051 836 L 5158 865 mt 5208 915 L 5208 865 mt 5158 915 L 5265 944 mt 5315 994 L 5315 944 mt 5265 994 L 5372 1023 mt 5422 1073 L 5422 1023 mt 5372 1073 L 5479 1102 mt 5529 1152 L 5529 1102 mt 5479 1152 L 5586 1182 mt 5636 1232 L 5636 1182 mt 5586 1232 L 5693 1261 mt 5743 1311 L 5743 1261 mt 5693 1311 L 5801 1340 mt 5851 1390 L 5851 1340 mt 5801 1390 L 5908 1419 mt 5958 1469 L 5958 1419 mt 5908 1469 L 6015 865 mt 6065 915 L 6065 865 mt 6015 915 L 6122 944 mt 6172 994 L 6172 944 mt 6122 994 L 6229 1023 mt 6279 1073 L 6279 1023 mt 6229 1073 L gr gs 898 388 5357 4226 MR c np gr 2910 5063 mt (true positives) s 568 3179 mt -90 rotate (false positives) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 1009 604 a Fm(\(b\))1084 79 y 10360626 8288501 2828615 12169625 36377313 39008583 startTexFig 1084 79 a %%BeginDocument: figures/12-lo-fn.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 302 217 6121 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1849 4849 mt (10) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2920 4849 mt (20) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3992 4849 mt (30) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5063 4849 mt (40) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6134 4849 mt (50) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 4085 mt 952 4085 L 6254 4085 mt 6200 4085 L 563 4165 mt (0.5) s 898 3557 mt 952 3557 L 6254 3557 mt 6200 3557 L 743 3637 mt (1) s 898 3029 mt 952 3029 L 6254 3029 mt 6200 3029 L 563 3109 mt (1.5) s 898 2501 mt 952 2501 L 6254 2501 mt 6200 2501 L 743 2581 mt (2) s 898 1972 mt 952 1972 L 6254 1972 mt 6200 1972 L 563 2052 mt (2.5) s 898 1444 mt 952 1444 L 6254 1444 mt 6200 1444 L 743 1524 mt (3) s 898 916 mt 952 916 L 6254 916 mt 6200 916 L 563 996 mt (3.5) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (4) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 107 0 107 0 107 0 107 0 108 264 107 0 107 -264 107 -265 107 0 107 -264 107 0 107 -264 108 -264 107 0 107 528 107 264 107 -792 107 0 107 264 107 0 108 264 107 264 107 -528 107 264 107 0 107 -264 107 -792 107 0 107 0 108 0 107 0 107 528 107 0 107 0 107 0 107 0 107 -264 108 -264 107 0 107 264 107 -264 107 -264 107 -528 107 0 107 0 108 528 107 -528 107 0 107 0 1005 4613 50 MP stroke gr gs 932 1899 5396 2788 MR c np 36 36 1005 4613 FO 36 36 1112 4613 FO 36 36 1219 4613 FO 36 36 1326 4085 FO 36 36 1434 4613 FO 36 36 1541 4613 FO 36 36 1648 4613 FO 36 36 1755 4085 FO 36 36 1862 3821 FO 36 36 1969 3557 FO 36 36 2076 3821 FO 36 36 2183 3821 FO 36 36 2291 3557 FO 36 36 2398 3293 FO 36 36 2505 3293 FO 36 36 2612 3293 FO 36 36 2719 3293 FO 36 36 2826 3293 FO 36 36 2933 3821 FO 36 36 3040 3821 FO 36 36 3148 3821 FO 36 36 3255 3821 FO 36 36 3362 3821 FO 36 36 3469 3029 FO 36 36 3576 2765 FO 36 36 3683 2765 FO 36 36 3790 3029 FO 36 36 3897 2501 FO 36 36 4004 2765 FO 36 36 4112 3029 FO 36 36 4219 3029 FO 36 36 4326 3293 FO 36 36 4433 3293 FO 36 36 4540 2501 FO 36 36 4647 2765 FO 36 36 4754 3293 FO 36 36 4861 3293 FO 36 36 4969 3029 FO 36 36 5076 2765 FO 36 36 5183 2765 FO 36 36 5290 2501 FO 36 36 5397 2501 FO 36 36 5504 2236 FO 36 36 5611 1972 FO 36 36 5718 1972 FO 36 36 5826 2236 FO 36 36 5933 2236 FO 36 36 6040 2236 FO 36 36 6147 2236 FO 36 36 6254 2236 FO gr gs 898 388 5357 4226 MR c np DA 107 0 107 -264 107 264 107 0 108 -264 107 -264 107 0 107 -264 107 0 107 0 107 0 107 0 108 -792 107 0 107 264 107 264 107 -264 107 0 107 -264 107 -264 108 264 107 264 107 -264 107 0 107 0 107 0 107 264 107 528 107 -792 108 -264 107 0 107 264 107 -264 107 -265 107 0 107 0 107 -528 108 -528 107 0 107 264 107 -528 107 0 107 0 107 0 107 -528 108 528 107 -528 107 -264 107 264 1005 4349 50 MP stroke SO gr gs 932 315 5396 4372 MR c np 980 4324 mt 1030 4374 L 1030 4324 mt 980 4374 L 1087 4588 mt 1137 4638 L 1137 4588 mt 1087 4638 L 1194 4324 mt 1244 4374 L 1244 4324 mt 1194 4374 L 1301 3796 mt 1351 3846 L 1351 3796 mt 1301 3846 L 1409 4324 mt 1459 4374 L 1459 4324 mt 1409 4374 L 1516 3796 mt 1566 3846 L 1566 3796 mt 1516 3846 L 1623 3796 mt 1673 3846 L 1673 3796 mt 1623 3846 L 1730 3796 mt 1780 3846 L 1780 3796 mt 1730 3846 L 1837 3796 mt 1887 3846 L 1887 3796 mt 1837 3846 L 1944 3268 mt 1994 3318 L 1994 3268 mt 1944 3318 L 2051 3532 mt 2101 3582 L 2101 3532 mt 2051 3582 L 2158 3532 mt 2208 3582 L 2208 3532 mt 2158 3582 L 2266 3004 mt 2316 3054 L 2316 3004 mt 2266 3054 L 2373 2476 mt 2423 2526 L 2423 2476 mt 2373 2526 L 2480 2476 mt 2530 2526 L 2530 2476 mt 2480 2526 L 2587 2476 mt 2637 2526 L 2637 2476 mt 2587 2526 L 2694 2211 mt 2744 2261 L 2744 2211 mt 2694 2261 L 2801 1947 mt 2851 1997 L 2851 1947 mt 2801 1997 L 2908 2211 mt 2958 2261 L 2958 2211 mt 2908 2261 L 3015 2211 mt 3065 2261 L 3065 2211 mt 3015 2261 L 3123 1947 mt 3173 1997 L 3173 1947 mt 3123 1997 L 3230 1155 mt 3280 1205 L 3280 1155 mt 3230 1205 L 3337 1683 mt 3387 1733 L 3387 1683 mt 3337 1733 L 3444 1947 mt 3494 1997 L 3494 1947 mt 3444 1997 L 3551 1947 mt 3601 1997 L 3601 1947 mt 3551 1997 L 3658 1947 mt 3708 1997 L 3708 1947 mt 3658 1997 L 3765 1947 mt 3815 1997 L 3815 1947 mt 3765 1997 L 3872 1683 mt 3922 1733 L 3922 1683 mt 3872 1733 L 3979 1947 mt 4029 1997 L 4029 1947 mt 3979 1997 L 4087 2211 mt 4137 2261 L 4137 2211 mt 4087 2261 L 4194 1947 mt 4244 1997 L 4244 1947 mt 4194 1997 L 4301 1683 mt 4351 1733 L 4351 1683 mt 4301 1733 L 4408 1683 mt 4458 1733 L 4458 1683 mt 4408 1733 L 4515 1419 mt 4565 1469 L 4565 1419 mt 4515 1469 L 4622 1683 mt 4672 1733 L 4672 1683 mt 4622 1733 L 4729 1947 mt 4779 1997 L 4779 1947 mt 4729 1997 L 4836 1947 mt 4886 1997 L 4886 1947 mt 4836 1997 L 4944 1155 mt 4994 1205 L 4994 1155 mt 4944 1205 L 5051 1155 mt 5101 1205 L 5101 1155 mt 5051 1205 L 5158 1155 mt 5208 1205 L 5208 1155 mt 5158 1205 L 5265 1155 mt 5315 1205 L 5315 1155 mt 5265 1205 L 5372 1155 mt 5422 1205 L 5422 1155 mt 5372 1205 L 5479 891 mt 5529 941 L 5529 891 mt 5479 941 L 5586 891 mt 5636 941 L 5636 891 mt 5586 941 L 5693 627 mt 5743 677 L 5743 627 mt 5693 677 L 5801 363 mt 5851 413 L 5851 363 mt 5801 413 L 5908 363 mt 5958 413 L 5958 363 mt 5908 413 L 6015 627 mt 6065 677 L 6065 627 mt 6015 677 L 6122 363 mt 6172 413 L 6172 363 mt 6122 413 L 6229 363 mt 6279 413 L 6279 363 mt 6229 413 L gr gs 898 388 5357 4226 MR c np gr 2599 5063 mt (approximate ranking) s 508 3221 mt -90 rotate (false negatives) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 710 a Fm(Figure)f(7:)23 b(\(a\))12 b(Av)o(erage)h(n)o(um)o(b)q(er)h (of)f(false)h(p)q(ositiv)o(es)h(as)e(a)g(function)i(of)e(true)g(p)q (ositiv)o(es)i(for)e(the)g(v)m(aria-)277 766 y(tional)g(metho)q(d)g (\(solid)h(line\))g(and)f(the)g(partially-exact)h(metho)q(d)f(\(dashed) g(line\).)20 b(\(b\))13 b(F)l(alse)277 823 y(negativ)o(es)j(in)h(the)g (set)f(of)g(top)g Fi(N)21 b Fm(appro)o(ximately)c(rank)o(ed)g (diseases.)24 b(In)17 b(b)q(oth)g(\014gures)g(12)277 879 y(p)q(ositiv)o(e)f(\014ndings)g(w)o(ere)f(treated)g(exactly)l(.)75 1076 y(tractable)h(CPC)f(cases.)22 b(Eigh)o(t)16 b(p)q(ositiv)o(e)h (\014ndings)g(w)o(ere)f(treated)f(exactly)i(in)f(the)g(sim)o(ulation)h (sho)o(wn)75 1132 y(in)f(this)g(\014gure.)k(Figure)15 b(7)g(displa)o(ys)h(the)g(results)f(when)h(12)e(p)q(ositiv)o(e)j (\014nding)f(w)o(ere)f(treated)g(exactly)l(.)146 1193 y(As)k(w)o(e)h(noted)g(earlier,)h(8)f(and)g(12)f(p)q(ositiv)o(e)i (\014ndings)g(comprise)f(a)g(signi\014can)o(t)h(fraction)e(of)h(the)75 1250 y(total)c(p)q(ositiv)o(e)h(\014ndings)g(for)f(the)g(tractable)g (CPC)g(cases,)g(and)h(th)o(us)f(it)g(is)h(imp)q(ortan)o(t)f(to)f(v)o (erify)i(that)75 1306 y(the)j(v)m(ariational)i(transformations)d(are)h (in)h(fact)f(con)o(tributing)h(to)f(the)g(accuracy)h(of)f(the)g(p)q (osterior)75 1363 y(appro)o(ximations)e(ab)q(o)o(v)o(e)h(and)f(b)q(ey)o (ond)h(the)g(exact)f(calculations.)32 b(W)l(e)18 b(did)i(this)f(b)o(y)f (comparing)h(the)75 1419 y(v)m(ariational)g(metho)q(d)e(to)g(a)g(metho) q(d)h(whic)o(h)h(w)o(e)e(call)i(the)e(\\partially-exact")h(metho)q(d)g (in)g(whic)o(h)h(the)75 1476 y(p)q(osterior)c(probabilities)i(w)o(ere)d (obtained)i(using)f(only)h(those)e(\014ndings)i(that)e(w)o(ere)h (treated)f(exactly)h(in)75 1532 y(the)j(v)m(ariational)g(calculations)h (\(i.e.,)f(using)g(only)g(those)f(\014ndings)i(that)e(w)o(ere)g(not)g (transformed\).)26 b(If)75 1589 y(the)19 b(v)m(ariational)g (transformations)e(did)j(not)e(con)o(tribute)h(to)f(the)h(accuracy)g (of)f(the)g(appro)o(ximation,)75 1645 y(then)h(the)f(p)q(erformance)h (of)f(the)g(partially-exact)i(metho)q(d)e(should)i(b)q(e)f(comparable)f (to)g(that)g(of)g(the)75 1701 y(v)m(ariational)f(metho)q(d.)465 1685 y Ft(7)508 1701 y Fm(Figure)f(6)g(and)h(Figure)f(7)g(clearly)h (indicate)h(that)d(this)i(is)g(not)f(the)g(case.)23 b(The)75 1758 y(di\013erence)16 b(in)f(accuracy)f(b)q(et)o(w)o(een)h(these)g (metho)q(ds)f(is)h(substan)o(tial)g(while)h(their)f(computational)g (load)75 1814 y(is)h(comparable)f(\(ab)q(out)g(0.1)f(seconds)i(on)f(a)g (433MHz)f(Dec)h(Alpha\).)146 1875 y(W)l(e)i(b)q(eliev)o(e)j(that)d(the) 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(ance)e(of)f(the)g(\014ndings.)954 2753 y Fn(18)p eop %%Page: 19 19 19 18 bop 431 -100 a Fq(V)-5 b(aria)m(tional)17 b(Pr)o(obabilistic)e (Inference)h(and)h(QMR-DT)627 79 y 10194856 8288501 3157524 12169625 36377313 39008583 startTexFig 627 79 a %%BeginDocument: figures/12-lo.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef 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bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 362 217 6061 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 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6254 388 mt 6200 388 L 623 468 mt (40) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 107 -105 107 79 107 -238 107 -26 108 53 107 53 107 26 107 26 107 53 107 79 107 0 107 80 108 -634 107 -79 107 52 107 80 107 -27 107 -53 107 53 107 27 108 79 107 79 107 -106 107 80 107 79 107 -106 107 -158 107 -27 107 -158 108 0 107 79 107 79 107 0 107 -105 107 0 107 79 107 -79 108 53 107 -27 107 53 107 -132 107 26 107 -158 107 0 107 0 108 53 107 -53 107 0 107 0 1005 4613 50 MP stroke gr gs 932 3589 5396 1098 MR c np 36 36 1005 4613 FO 36 36 1112 4613 FO 36 36 1219 4613 FO 36 36 1326 4560 FO 36 36 1434 4613 FO 36 36 1541 4613 FO 36 36 1648 4613 FO 36 36 1755 4455 FO 36 36 1862 4481 FO 36 36 1969 4349 FO 36 36 2076 4402 FO 36 36 2183 4375 FO 36 36 2291 4428 FO 36 36 2398 4349 FO 36 36 2505 4428 FO 36 36 2612 4428 FO 36 36 2719 4323 FO 36 36 2826 4323 FO 36 36 2933 4402 FO 36 36 3040 4481 FO 36 36 3148 4481 FO 36 36 3255 4323 FO 36 36 3362 4296 FO 36 36 3469 4138 FO 36 36 3576 4032 FO 36 36 3683 4111 FO 36 36 3790 4191 FO 36 36 3897 4085 FO 36 36 4004 4164 FO 36 36 4112 4243 FO 36 36 4219 4270 FO 36 36 4326 4323 FO 36 36 4433 4270 FO 36 36 4540 4243 FO 36 36 4647 4323 FO 36 36 4754 4375 FO 36 36 4861 4296 FO 36 36 4969 3662 FO 36 36 5076 3742 FO 36 36 5183 3742 FO 36 36 5290 3821 FO 36 36 5397 3874 FO 36 36 5504 3900 FO 36 36 5611 3926 FO 36 36 5718 3979 FO 36 36 5826 4032 FO 36 36 5933 4006 FO 36 36 6040 3768 FO 36 36 6147 3847 FO 36 36 6254 3742 FO gr gs 898 388 5357 4226 MR c np DA 107 79 107 79 107 -554 107 79 108 79 107 79 107 80 107 79 107 79 107 79 107 79 107 -1452 108 -132 107 79 107 80 107 79 107 79 107 -264 107 79 107 79 108 -924 107 79 107 80 107 79 107 79 107 26 107 80 107 -291 107 -185 108 80 107 79 107 -53 107 79 107 79 107 -1056 107 -79 107 79 108 -238 107 -52 107 52 107 -52 107 -159 107 -105 107 79 107 -79 108 79 107 -132 107 -53 107 26 1005 4587 50 MP stroke SO gr gs 932 738 5396 3949 MR c np 980 4562 mt 1030 4612 L 1030 4562 mt 980 4612 L 1087 4588 mt 1137 4638 L 1137 4588 mt 1087 4638 L 1194 4535 mt 1244 4585 L 1244 4535 mt 1194 4585 L 1301 4403 mt 1351 4453 L 1351 4403 mt 1301 4453 L 1409 4482 mt 1459 4532 L 1459 4482 mt 1409 4532 L 1516 4403 mt 1566 4453 L 1566 4403 mt 1516 4453 L 1623 4482 mt 1673 4532 L 1673 4482 mt 1623 4532 L 1730 4377 mt 1780 4427 L 1780 4377 mt 1730 4427 L 1837 4218 mt 1887 4268 L 1887 4218 mt 1837 4268 L 1944 4166 mt 1994 4216 L 1994 4166 mt 1944 4216 L 2051 4218 mt 2101 4268 L 2101 4218 mt 2051 4268 L 2158 4166 mt 2208 4216 L 2208 4166 mt 2158 4216 L 2266 3928 mt 2316 3978 L 2316 3928 mt 2266 3978 L 2373 4007 mt 2423 4057 L 2423 4007 mt 2373 4057 L 2480 3928 mt 2530 3978 L 2530 3928 mt 2480 3978 L 2587 2872 mt 2637 2922 L 2637 2872 mt 2587 2922 L 2694 2951 mt 2744 3001 L 2744 2951 mt 2694 3001 L 2801 3030 mt 2851 3080 L 2851 3030 mt 2801 3080 L 2908 2977 mt 2958 3027 L 2958 2977 mt 2908 3027 L 3015 3056 mt 3065 3106 L 3065 3056 mt 3015 3106 L 3123 3136 mt 3173 3186 L 3173 3136 mt 3123 3186 L 3230 2951 mt 3280 3001 L 3280 2951 mt 3230 3001 L 3337 2660 mt 3387 2710 L 3387 2660 mt 3337 2710 L 3444 2740 mt 3494 2790 L 3494 2740 mt 3444 2790 L 3551 2766 mt 3601 2816 L 3601 2766 mt 3551 2816 L 3658 2845 mt 3708 2895 L 3708 2845 mt 3658 2895 L 3765 2924 mt 3815 2974 L 3815 2924 mt 3765 2974 L 3872 3004 mt 3922 3054 L 3922 3004 mt 3872 3054 L 3979 3083 mt 4029 3133 L 4029 3083 mt 3979 3133 L 4087 2159 mt 4137 2209 L 4137 2159 mt 4087 2209 L 4194 2238 mt 4244 2288 L 4244 2238 mt 4194 2288 L 4301 2317 mt 4351 2367 L 4351 2317 mt 4301 2367 L 4408 2053 mt 4458 2103 L 4458 2053 mt 4408 2103 L 4515 2132 mt 4565 2182 L 4565 2132 mt 4515 2182 L 4622 2211 mt 4672 2261 L 4672 2211 mt 4622 2261 L 4729 2291 mt 4779 2341 L 4779 2291 mt 4729 2341 L 4836 2370 mt 4886 2420 L 4886 2370 mt 4836 2420 L 4944 2238 mt 4994 2288 L 4994 2238 mt 4944 2288 L 5051 786 mt 5101 836 L 5101 786 mt 5051 836 L 5158 865 mt 5208 915 L 5208 865 mt 5158 915 L 5265 944 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%000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 %000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 %000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 0 6912 5185 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1819 4849 mt (0.2) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2890 4849 mt (0.4) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3962 4849 mt (0.6) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5033 4849 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6194 4849 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 563 3848 mt (0.2) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 563 3003 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6253 388 FO 36 36 6252 388 FO 36 36 6251 388 FO 36 36 6251 482 FO 36 36 6251 388 FO 36 36 6251 388 FO 36 36 6248 388 FO 36 36 6247 388 FO 36 36 6247 602 FO 36 36 6246 388 FO 36 36 6244 388 FO 36 36 6244 640 FO 36 36 6240 388 FO 36 36 6235 388 FO 36 36 6227 1324 FO 36 36 6225 1340 FO 36 36 6219 388 FO 36 36 6206 390 FO 36 36 6200 546 FO 36 36 6197 392 FO 36 36 6192 699 FO 36 36 6189 388 FO 36 36 6187 388 FO 36 36 6183 388 FO 36 36 6180 421 FO 36 36 6178 402 FO 36 36 6174 391 FO 36 36 6168 390 FO 36 36 6158 388 FO 36 36 6140 391 FO 36 36 6117 391 FO 36 36 6114 389 FO 36 36 6112 388 FO 36 36 6106 390 FO 36 36 6093 451 FO 36 36 6087 388 FO 36 36 6031 439 FO 36 36 6019 396 FO 36 36 6000 433 FO 36 36 6000 394 FO 36 36 5951 399 FO gs 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3159 2851 FO 36 36 2421 3381 FO 36 36 2127 3641 FO 36 36 1746 3948 FO 36 36 1655 4016 FO 36 36 1644 4065 FO 36 36 1522 4122 FO 36 36 1296 4299 FO 36 36 1287 4289 FO 36 36 1265 4304 FO 36 36 1154 4411 FO 36 36 1149 4401 FO 36 36 1138 4421 FO 36 36 1131 4424 FO 36 36 1115 4442 FO 36 36 1115 4428 FO 36 36 1112 4441 FO 36 36 1065 4482 FO 36 36 1059 4486 FO 36 36 1056 4479 FO 36 36 1031 4508 FO 36 36 1019 4510 FO 36 36 1009 4518 FO 36 36 1009 4525 FO 36 36 1004 4529 FO 36 36 1004 4529 FO 36 36 1003 4525 FO 36 36 997 4536 FO 36 36 996 4535 FO 36 36 993 4531 FO 36 36 991 4534 FO 36 36 979 4549 FO 36 36 974 4553 FO 36 36 972 4554 FO 36 36 972 4555 FO 36 36 970 4557 FO 36 36 968 4554 FO 36 36 966 4556 FO 36 36 965 4558 FO 36 36 963 4562 FO 36 36 960 4564 FO 36 36 959 4565 FO 36 36 956 4568 FO 36 36 955 4568 FO 36 36 954 4569 FO 36 36 953 4570 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6254 4329 FO 36 36 6254 621 FO 36 36 6240 4589 FO 36 36 6238 712 FO 36 36 6233 656 FO 36 36 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4244 FO 36 36 1283 4307 FO 36 36 1265 4323 FO 36 36 1265 4327 FO 36 36 1182 4391 FO 36 36 1154 4413 FO 36 36 1121 4431 FO 36 36 1093 4455 FO 36 36 1039 4498 FO 36 36 1039 4503 FO 36 36 1010 4524 FO 36 36 1007 4527 FO 36 36 998 4536 FO 36 36 990 4541 FO 36 36 975 4553 FO 36 36 974 4554 FO 36 36 969 4557 FO 36 36 962 4563 FO 36 36 960 4564 FO 36 36 960 4562 FO 36 36 959 4565 FO 36 36 950 4572 FO 36 36 948 4574 FO 36 36 946 4575 FO 36 36 945 4576 FO 36 36 943 4578 FO 36 36 942 4578 FO 36 36 939 4580 FO 36 36 936 4582 FO 36 36 935 4583 FO 36 36 934 4585 FO 36 36 934 4584 FO 36 36 933 4585 FO 36 36 933 4584 FO 36 36 932 4586 FO 36 36 928 4589 FO 36 36 927 4590 FO 36 36 926 4591 FO 36 36 925 4592 FO 36 36 924 4592 FO 36 36 923 4593 FO gs 898 388 5357 4226 MR c np gr 36 36 5432 1020 FO 36 36 4383 1844 FO 36 36 3957 2184 FO 36 36 2678 3199 FO 36 36 2674 3226 FO 36 36 2285 3501 FO 36 36 1840 3846 FO 36 36 1399 4188 FO 36 36 1369 4242 FO 36 36 1339 4256 FO 36 36 1259 4331 FO 36 36 1199 4375 FO 36 36 1157 4407 FO 36 36 1144 4414 FO 36 36 1129 4429 FO 36 36 1091 4454 FO 36 36 1067 4479 FO 36 36 1059 4486 FO 36 36 1034 4506 FO 36 36 1030 4509 FO 36 36 1009 4526 FO 36 36 1008 4526 FO 36 36 1001 4531 FO 36 36 997 4535 FO 36 36 992 4539 FO 36 36 985 4543 FO 36 36 982 4547 FO 36 36 981 4548 FO 36 36 972 4553 FO 36 36 971 4555 FO 36 36 969 4557 FO 36 36 969 4556 FO 36 36 968 4557 FO 36 36 968 4557 FO 36 36 967 4558 FO 36 36 966 4557 FO 36 36 964 4560 FO 36 36 957 4566 FO 36 36 955 4567 FO 36 36 953 4569 FO 36 36 945 4575 FO 36 36 944 4577 FO 36 36 940 4580 FO 36 36 937 4583 FO 36 36 936 4583 FO 36 36 934 4585 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6254 388 FO 36 36 6254 389 FO 36 36 6254 388 FO 36 36 6254 432 FO 36 36 6254 726 FO 36 36 6254 390 FO 36 36 6254 388 FO 36 36 6254 391 FO 36 36 6254 4248 FO 36 36 6254 388 FO 36 36 6253 388 FO 36 36 6253 391 FO 36 36 6253 3330 FO 36 36 6253 3588 FO 36 36 6251 4515 FO 36 36 6251 4167 FO 36 36 6251 4596 FO 36 36 6249 4604 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6208 388 FO 36 36 6199 3600 FO 36 36 6187 394 FO 36 36 6186 4589 FO 36 36 6175 388 FO 36 36 6163 4564 FO 36 36 6139 388 FO 36 36 6111 4582 FO 36 36 6105 390 FO 36 36 6103 3688 FO 36 36 6083 1172 FO 36 36 6076 447 FO 36 36 6054 2482 FO 36 36 6042 390 FO 36 36 6037 4206 FO 36 36 6031 4563 FO 36 36 6025 390 FO 36 36 6010 4420 FO 36 36 5979 390 FO 36 36 5962 390 FO 36 36 5951 2136 FO 36 36 5916 453 FO 36 36 5900 398 FO 36 36 5868 388 FO 36 36 5858 4493 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6251 388 FO 36 36 6250 399 FO 36 36 6244 388 FO 36 36 6234 429 FO 36 36 6232 413 FO 36 36 6222 426 FO 36 36 6221 422 FO 36 36 6217 392 FO 36 36 6216 472 FO 36 36 6214 428 FO 36 36 6212 432 FO 36 36 6187 453 FO 36 36 6170 449 FO 36 36 6167 578 FO 36 36 6164 473 FO 36 36 6023 606 FO 36 36 5916 981 FO 36 36 5892 711 FO 36 36 5876 388 FO 36 36 5872 735 FO 36 36 5839 1288 FO 36 36 5683 2064 FO 36 36 5569 1038 FO 36 36 5546 3238 FO 36 36 5529 1084 FO 36 36 5339 482 FO 36 36 5112 1392 FO 36 36 5091 2344 FO 36 36 4843 2957 FO 36 36 4378 1016 FO 36 36 4064 3740 FO 36 36 4040 2543 FO 36 36 3743 3800 FO 36 36 3734 3665 FO 36 36 3522 1805 FO 36 36 3101 4114 FO 36 36 2992 3293 FO 36 36 2970 2875 FO 36 36 2897 3801 FO 36 36 2889 3902 FO 36 36 2837 3265 FO 36 36 2761 3633 FO 36 36 2699 3665 FO 36 36 2670 3393 FO 36 36 2460 4248 FO 36 36 2421 3424 FO 36 36 2396 2751 FO 36 36 2360 3504 FO 36 36 2328 3635 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6249 395 FO 36 36 6114 511 FO 36 36 5841 718 FO 36 36 5204 1233 FO 36 36 3345 2669 FO 36 36 2016 3726 FO 36 36 1991 3763 FO 36 36 1373 4244 FO 36 36 1365 4245 FO 36 36 1278 4319 FO 36 36 1277 4317 FO 36 36 1208 4367 FO 36 36 1174 4394 FO 36 36 1170 4400 FO 36 36 1097 4456 FO 36 36 1052 4490 FO 36 36 1052 4493 FO 36 36 1047 4495 FO 36 36 1037 4504 FO 36 36 1026 4512 FO 36 36 1021 4516 FO 36 36 1020 4518 FO 36 36 1020 4517 FO 36 36 1002 4531 FO 36 36 999 4535 FO 36 36 998 4534 FO 36 36 998 4534 FO 36 36 996 4536 FO 36 36 994 4537 FO 36 36 994 4537 FO 36 36 992 4539 FO 36 36 989 4541 FO 36 36 989 4542 FO 36 36 986 4543 FO 36 36 983 4544 FO 36 36 982 4548 FO 36 36 978 4550 FO 36 36 977 4551 FO 36 36 971 4557 FO 36 36 968 4561 FO 36 36 963 4560 FO 36 36 959 4565 FO 36 36 958 4565 FO 36 36 958 4567 FO 36 36 957 4566 FO 36 36 955 4567 FO 36 36 954 4569 FO gs 898 388 5357 4226 MR c np gr 36 36 5950 582 FO 36 36 5168 1278 FO 36 36 4007 2108 FO 36 36 3851 2242 FO 36 36 3827 2273 FO 36 36 3650 2408 FO 36 36 2872 3055 FO 36 36 2534 3250 FO 36 36 1486 4139 FO 36 36 1439 4190 FO 36 36 1335 4259 FO 36 36 1319 4270 FO 36 36 1269 4316 FO 36 36 1222 4351 FO 36 36 1207 4371 FO 36 36 1179 4393 FO 36 36 1170 4403 FO 36 36 1168 4381 FO 36 36 1166 4406 FO 36 36 1162 4406 FO 36 36 1160 4381 FO 36 36 1150 4425 FO 36 36 1142 4419 FO 36 36 1140 4418 FO 36 36 1125 4436 FO 36 36 1121 4437 FO 36 36 1103 4461 FO 36 36 1092 4459 FO 36 36 1064 4478 FO 36 36 1062 4484 FO 36 36 1061 4483 FO 36 36 1061 4479 FO 36 36 1052 4492 FO 36 36 1052 4474 FO 36 36 1042 4504 FO 36 36 1042 4498 FO 36 36 1020 4519 FO 36 36 1020 4516 FO 36 36 1019 4555 FO 36 36 1015 4526 FO 36 36 1013 4521 FO 36 36 1007 4527 FO 36 36 1002 4531 FO 36 36 994 4539 FO 36 36 992 4538 FO 36 36 990 4540 FO 36 36 989 4547 FO 36 36 985 4544 FO 36 36 984 4544 FO 36 36 982 4547 FO gs 898 388 5357 4226 MR c np gr 36 36 5771 777 FO 36 36 5350 1169 FO 36 36 5309 1111 FO 36 36 3517 2612 FO 36 36 3485 2536 FO 36 36 3451 2538 FO 36 36 3382 2550 FO 36 36 2567 3257 FO 36 36 1571 4074 FO 36 36 1499 4095 FO 36 36 1466 4152 FO 36 36 1371 4199 FO 36 36 1341 4261 FO 36 36 1316 4294 FO 36 36 1283 4277 FO 36 36 1261 4313 FO 36 36 1248 4340 FO 36 36 1236 4366 FO 36 36 1167 4397 FO 36 36 1120 4430 FO 36 36 1119 4439 FO 36 36 1118 4428 FO 36 36 1115 4438 FO 36 36 1104 4445 FO 36 36 1098 4449 FO 36 36 1092 4455 FO 36 36 1077 4467 FO 36 36 1068 4482 FO 36 36 1067 4475 FO 36 36 1055 4483 FO 36 36 1051 4493 FO 36 36 1046 4502 FO 36 36 1044 4496 FO 36 36 1038 4505 FO 36 36 1027 4517 FO 36 36 1024 4512 FO 36 36 1018 4509 FO 36 36 1017 4510 FO 36 36 1007 4524 FO 36 36 1005 4528 FO 36 36 1005 4525 FO 36 36 1004 4529 FO 36 36 1000 4529 FO 36 36 1000 4527 FO 36 36 997 4534 FO 36 36 994 4537 FO 36 36 987 4540 FO 36 36 983 4542 FO 36 36 979 4546 FO 36 36 979 4547 FO gs 898 388 5357 4226 MR c np gr 36 36 6251 403 FO 36 36 6085 445 FO 36 36 5134 933 FO 36 36 4863 1136 FO 36 36 3838 2178 FO 36 36 3552 1724 FO 36 36 3396 2304 FO 36 36 2509 3364 FO 36 36 2226 3381 FO 36 36 2039 4236 FO 36 36 1872 4257 FO 36 36 1865 3620 FO 36 36 1849 3374 FO 36 36 1627 4262 FO 36 36 1461 4441 FO 36 36 1425 4385 FO 36 36 1221 4484 FO 36 36 1206 4392 FO 36 36 1170 4521 FO 36 36 1156 4525 FO 36 36 1138 4495 FO 36 36 1132 4483 FO 36 36 1129 4477 FO 36 36 1129 4500 FO 36 36 1125 4433 FO 36 36 1117 4484 FO 36 36 1097 4529 FO 36 36 1096 4529 FO 36 36 1096 4538 FO 36 36 1088 4549 FO 36 36 1087 4545 FO 36 36 1086 4520 FO 36 36 1081 4554 FO 36 36 1081 4511 FO 36 36 1074 4548 FO 36 36 1068 4497 FO 36 36 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36 36 971 4561 FO 36 36 971 4556 FO 36 36 968 4558 FO 36 36 967 4558 FO 36 36 964 4561 FO 36 36 962 4562 FO 36 36 959 4572 FO 36 36 956 4567 FO 36 36 955 4575 FO gs 898 388 5357 4226 MR c np gr 36 36 6190 388 FO 36 36 5641 517 FO 36 36 4294 393 FO 36 36 4278 404 FO 36 36 4200 524 FO 36 36 3577 391 FO 36 36 2901 538 FO 36 36 2872 399 FO 36 36 2466 532 FO 36 36 2448 390 FO 36 36 2321 483 FO 36 36 2162 392 FO 36 36 2130 712 FO 36 36 2073 1135 FO 36 36 2032 389 FO 36 36 2025 2574 FO 36 36 1809 4096 FO 36 36 1758 504 FO 36 36 1735 388 FO 36 36 1609 3454 FO 36 36 1583 3722 FO 36 36 1568 425 FO 36 36 1563 389 FO 36 36 1404 4376 FO 36 36 1335 4479 FO 36 36 1332 4237 FO 36 36 1331 962 FO 36 36 1318 3685 FO 36 36 1304 505 FO 36 36 1267 892 FO 36 36 1255 733 FO 36 36 1230 3343 FO 36 36 1224 479 FO 36 36 1219 1444 FO 36 36 1207 442 FO 36 36 1195 522 FO 36 36 1193 509 FO 36 36 1173 2980 FO 36 36 1164 4447 FO 36 36 1152 455 FO 36 36 1143 4400 FO 36 36 1141 474 FO 36 36 1140 597 FO 36 36 1126 416 FO 36 36 1119 3753 FO 36 36 1118 3590 FO 36 36 1112 2718 FO 36 36 1110 1966 FO 36 36 1093 3866 FO 36 36 1087 4446 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6061 527 FO 36 36 5578 884 FO 36 36 5250 1263 FO 36 36 4247 1998 FO 36 36 4193 2027 FO 36 36 3870 2324 FO 36 36 3506 2630 FO 36 36 2897 3095 FO 36 36 2630 3233 FO 36 36 2476 3271 FO 36 36 2264 3527 FO 36 36 1917 3788 FO 36 36 1789 3877 FO 36 36 1700 3962 FO 36 36 1634 4033 FO 36 36 1618 4084 FO 36 36 1517 4136 FO 36 36 1507 4139 FO 36 36 1488 4122 FO 36 36 1485 4151 FO 36 36 1431 4210 FO 36 36 1348 4267 FO 36 36 1344 4250 FO 36 36 1321 4279 FO 36 36 1295 4298 FO 36 36 1294 4302 FO 36 36 1255 4329 FO 36 36 1229 4321 FO 36 36 1198 4368 FO 36 36 1193 4385 FO 36 36 1150 4413 FO 36 36 1126 4436 FO 36 36 1119 4436 FO 36 36 1119 4428 FO 36 36 1113 4447 FO 36 36 1098 4454 FO 36 36 1098 4444 FO 36 36 1093 4458 FO 36 36 1090 4460 FO 36 36 1083 4458 FO 36 36 1078 4476 FO 36 36 1066 4474 FO 36 36 1062 4476 FO 36 36 1059 4494 FO 36 36 1056 4498 FO 36 36 1054 4491 FO 36 36 1054 4489 FO 36 36 1044 4498 FO 36 36 1024 4516 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 4630 1713 FO 36 36 3645 2473 FO 36 36 2467 3375 FO 36 36 2246 3535 FO 36 36 1592 4081 FO 36 36 1487 4156 FO 36 36 1440 4186 FO 36 36 1264 4337 FO 36 36 1213 4365 FO 36 36 1212 4362 FO 36 36 1172 4397 FO 36 36 1140 4428 FO 36 36 1138 4424 FO 36 36 1137 4431 FO 36 36 1106 4449 FO 36 36 1100 4460 FO 36 36 1094 4459 FO 36 36 1088 4471 FO 36 36 1084 4466 FO 36 36 1084 4467 FO 36 36 1070 4479 FO 36 36 1046 4500 FO 36 36 1037 4503 FO 36 36 1020 4517 FO 36 36 1016 4522 FO 36 36 1015 4523 FO 36 36 1014 4522 FO 36 36 1012 4523 FO 36 36 1011 4524 FO 36 36 1009 4526 FO 36 36 1009 4526 FO 36 36 990 4543 FO 36 36 985 4545 FO 36 36 971 4556 FO 36 36 963 4562 FO 36 36 958 4568 FO 36 36 958 4567 FO 36 36 957 4567 FO 36 36 956 4567 FO 36 36 954 4569 FO 36 36 953 4569 FO 36 36 953 4572 FO 36 36 953 4570 FO 36 36 952 4571 FO 36 36 950 4572 FO 36 36 949 4572 FO 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/rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 0 0 6912 5185 MR c np 88 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1819 4849 mt (0.2) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2890 4849 mt (0.4) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3962 4849 mt (0.6) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5033 4849 mt (0.8) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6194 4849 mt (1) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 3768 mt 952 3768 L 6254 3768 mt 6200 3768 L 563 3848 mt (0.2) s 898 2923 mt 952 2923 L 6254 2923 mt 6200 2923 L 563 3003 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6175 452 FO 36 36 5905 674 FO 36 36 5347 1266 FO 36 36 4218 2023 FO 36 36 4131 2064 FO 36 36 3533 2504 FO 36 36 3407 2608 FO 36 36 3325 2721 FO 36 36 3134 2803 FO 36 36 2201 3596 FO 36 36 2058 3724 FO 36 36 1844 3838 FO 36 36 1736 3957 FO 36 36 1645 4008 FO 36 36 1487 4128 FO 36 36 1283 4305 FO 36 36 1262 4324 FO 36 36 1213 4364 FO 36 36 1212 4391 FO 36 36 1158 4407 FO 36 36 1140 4425 FO 36 36 1139 4462 FO 36 36 1094 4462 FO 36 36 1087 4469 FO 36 36 1048 4501 FO 36 36 1047 4495 FO 36 36 1044 4498 FO 36 36 1043 4499 FO 36 36 1036 4501 FO 36 36 1035 4503 FO 36 36 1024 4514 FO 36 36 1008 4526 FO 36 36 1004 4534 FO 36 36 1001 4532 FO 36 36 988 4544 FO 36 36 981 4548 FO 36 36 974 4551 FO 36 36 974 4553 FO 36 36 968 4561 FO 36 36 965 4561 FO 36 36 964 4560 FO 36 36 958 4567 FO 36 36 957 4565 FO 36 36 956 4567 FO 36 36 955 4567 FO 36 36 955 4570 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 5557 931 FO 36 36 3690 2322 FO 36 36 3159 2851 FO 36 36 2421 3381 FO 36 36 2127 3641 FO 36 36 1746 3948 FO 36 36 1655 4016 FO 36 36 1644 4065 FO 36 36 1522 4122 FO 36 36 1296 4299 FO 36 36 1287 4289 FO 36 36 1265 4304 FO 36 36 1154 4411 FO 36 36 1149 4401 FO 36 36 1138 4421 FO 36 36 1131 4424 FO 36 36 1115 4442 FO 36 36 1115 4428 FO 36 36 1112 4441 FO 36 36 1065 4482 FO 36 36 1059 4486 FO 36 36 1056 4479 FO 36 36 1031 4508 FO 36 36 1019 4510 FO 36 36 1009 4518 FO 36 36 1009 4525 FO 36 36 1004 4529 FO 36 36 1004 4529 FO 36 36 1003 4525 FO 36 36 997 4536 FO 36 36 996 4535 FO 36 36 993 4531 FO 36 36 991 4534 FO 36 36 979 4549 FO 36 36 974 4553 FO 36 36 972 4554 FO 36 36 972 4555 FO 36 36 970 4557 FO 36 36 968 4554 FO 36 36 966 4556 FO 36 36 965 4558 FO 36 36 963 4562 FO 36 36 960 4564 FO 36 36 959 4565 FO 36 36 956 4568 FO 36 36 955 4568 FO 36 36 954 4569 FO 36 36 953 4570 FO gs 898 388 5357 4226 MR c np gr 36 36 6239 391 FO 36 36 3884 2188 FO 36 36 3095 2815 FO 36 36 2241 3582 FO 36 36 2143 3638 FO 36 36 2134 3654 FO 36 36 2085 3651 FO 36 36 2037 3692 FO 36 36 1970 3779 FO 36 36 1799 3920 FO 36 36 1779 3916 FO 36 36 1654 3997 FO 36 36 1648 4013 FO 36 36 1557 4099 FO 36 36 1474 4174 FO 36 36 1434 4165 FO 36 36 1419 4193 FO 36 36 1356 4264 FO 36 36 1330 4251 FO 36 36 1325 4256 FO 36 36 1299 4318 FO 36 36 1261 4315 FO 36 36 1235 4338 FO 36 36 1227 4334 FO 36 36 1197 4386 FO 36 36 1195 4382 FO 36 36 1194 4379 FO 36 36 1192 4382 FO 36 36 1185 4387 FO 36 36 1168 4389 FO 36 36 1157 4414 FO 36 36 1134 4422 FO 36 36 1131 4413 FO 36 36 1111 4435 FO 36 36 1105 4444 FO 36 36 1080 4476 FO 36 36 1076 4471 FO 36 36 1075 4480 FO 36 36 1075 4467 FO 36 36 1071 4472 FO 36 36 1062 4480 FO 36 36 1055 4487 FO 36 36 1055 4197 FO 36 36 1050 4493 FO 36 36 1037 4497 FO 36 36 1036 4500 FO 36 36 1031 4507 FO 36 36 1029 4511 FO 36 36 1022 4515 FO 36 36 1010 4524 FO gs 898 388 5357 4226 MR c np gr 36 36 6159 483 FO 36 36 5742 807 FO 36 36 5465 992 FO 36 36 4626 1754 FO 36 36 2868 3059 FO 36 36 2600 3367 FO 36 36 2201 3582 FO 36 36 2062 3724 FO 36 36 1686 4002 FO 36 36 1588 4166 FO 36 36 1411 4209 FO 36 36 1371 4231 FO 36 36 1336 4268 FO 36 36 1285 4295 FO 36 36 1280 4315 FO 36 36 1227 4346 FO 36 36 1220 4364 FO 36 36 1217 4361 FO 36 36 1200 4373 FO 36 36 1186 4389 FO 36 36 1143 4419 FO 36 36 1139 4428 FO 36 36 1135 4430 FO 36 36 1097 4451 FO 36 36 1093 4464 FO 36 36 1091 4466 FO 36 36 1059 4491 FO 36 36 1056 4491 FO 36 36 1049 4494 FO 36 36 1039 4502 FO 36 36 1038 4500 FO 36 36 1034 4503 FO 36 36 1026 4509 FO 36 36 1022 4514 FO 36 36 1021 4516 FO 36 36 1016 4516 FO 36 36 1012 4520 FO 36 36 1012 4541 FO 36 36 1001 4540 FO 36 36 1000 4540 FO 36 36 998 4534 FO 36 36 992 4534 FO 36 36 991 4542 FO 36 36 991 4540 FO 36 36 991 4550 FO 36 36 985 4542 FO 36 36 978 4550 FO 36 36 976 4550 FO 36 36 975 4552 FO 36 36 974 4543 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 389 FO 36 36 3890 2198 FO 36 36 3885 2220 FO 36 36 2946 2948 FO 36 36 2827 3051 FO 36 36 2819 3149 FO 36 36 2540 3280 FO 36 36 2532 3298 FO 36 36 2433 3399 FO 36 36 1837 3908 FO 36 36 1835 3869 FO 36 36 1792 3896 FO 36 36 1728 3940 FO 36 36 1547 4098 FO 36 36 1477 4144 FO 36 36 1344 4261 FO 36 36 1342 4264 FO 36 36 1339 4261 FO 36 36 1287 4310 FO 36 36 1233 4339 FO 36 36 1208 4369 FO 36 36 1204 4367 FO 36 36 1188 4383 FO 36 36 1143 4414 FO 36 36 1137 4420 FO 36 36 1136 4425 FO 36 36 1110 4432 FO 36 36 1075 4472 FO 36 36 1070 4484 FO 36 36 1065 4492 FO 36 36 1057 4489 FO 36 36 1057 4487 FO 36 36 1055 4486 FO 36 36 1049 4494 FO 36 36 1044 4493 FO 36 36 1042 4500 FO 36 36 1040 4502 FO 36 36 1039 4504 FO 36 36 1035 4505 FO 36 36 1034 4505 FO 36 36 1034 4506 FO 36 36 1033 4509 FO 36 36 1028 4511 FO 36 36 1025 4514 FO 36 36 1023 4514 FO 36 36 1013 4518 FO 36 36 1008 4526 FO 36 36 1007 4527 FO 36 36 1004 4529 FO 36 36 1003 4534 FO gs 898 388 5357 4226 MR c np gr 36 36 5713 817 FO 36 36 5410 1094 FO 36 36 4863 1461 FO 36 36 4240 2009 FO 36 36 3923 2311 FO 36 36 3272 2623 FO 36 36 3172 2882 FO 36 36 2569 3348 FO 36 36 2535 3316 FO 36 36 2315 3530 FO 36 36 1896 3817 FO 36 36 1885 3869 FO 36 36 1349 4239 FO 36 36 1206 4369 FO 36 36 1202 4365 FO 36 36 1177 4398 FO 36 36 1155 4410 FO 36 36 1145 4412 FO 36 36 1140 4422 FO 36 36 1117 4425 FO 36 36 1087 4466 FO 36 36 1080 4469 FO 36 36 1073 4476 FO 36 36 1054 4496 FO 36 36 1050 4498 FO 36 36 1047 4496 FO 36 36 1044 4506 FO 36 36 1040 4502 FO 36 36 1036 4506 FO 36 36 1021 4525 FO 36 36 1020 4519 FO 36 36 1019 4518 FO 36 36 1011 4524 FO 36 36 1008 4523 FO 36 36 1002 4531 FO 36 36 995 4539 FO 36 36 992 4538 FO 36 36 992 4539 FO 36 36 991 4540 FO 36 36 990 4540 FO 36 36 985 4544 FO 36 36 983 4549 FO 36 36 975 4554 FO 36 36 971 4556 FO 36 36 967 4561 FO 36 36 965 4562 FO 36 36 965 4560 FO 36 36 964 4560 FO gs 898 388 5357 4226 MR c np gr 36 36 5964 642 FO 36 36 2120 3614 FO 36 36 1484 4152 FO 36 36 1358 4255 FO 36 36 1241 4343 FO 36 36 1240 4344 FO 36 36 1206 4370 FO 36 36 1196 4379 FO 36 36 1190 4371 FO 36 36 1136 4427 FO 36 36 1078 4471 FO 36 36 1074 4474 FO 36 36 1055 4489 FO 36 36 1047 4496 FO 36 36 1030 4509 FO 36 36 1028 4511 FO 36 36 1025 4513 FO 36 36 1024 4514 FO 36 36 1015 4521 FO 36 36 1014 4523 FO 36 36 1013 4526 FO 36 36 1001 4532 FO 36 36 999 4534 FO 36 36 991 4540 FO 36 36 989 4542 FO 36 36 977 4550 FO 36 36 974 4554 FO 36 36 971 4555 FO 36 36 970 4556 FO 36 36 968 4558 FO 36 36 959 4566 FO 36 36 952 4571 FO 36 36 950 4572 FO 36 36 950 4572 FO 36 36 949 4572 FO 36 36 948 4574 FO 36 36 945 4576 FO 36 36 944 4578 FO 36 36 944 4578 FO 36 36 943 4578 FO 36 36 939 4581 FO 36 36 938 4581 FO 36 36 937 4583 FO 36 36 935 4584 FO 36 36 934 4584 FO 36 36 933 4586 FO gs 898 388 5357 4226 MR c np gr 36 36 5834 719 FO 36 36 4839 1562 FO 36 36 4611 1690 FO 36 36 3852 2390 FO 36 36 3694 2407 FO 36 36 3474 2564 FO 36 36 3101 2835 FO 36 36 2736 3137 FO 36 36 2540 3293 FO 36 36 2261 3586 FO 36 36 2175 3596 FO 36 36 2001 3817 FO 36 36 1780 3972 FO 36 36 1768 3922 FO 36 36 1694 4024 FO 36 36 1684 3959 FO 36 36 1617 4048 FO 36 36 1613 4041 FO 36 36 1559 4109 FO 36 36 1452 4153 FO 36 36 1413 4203 FO 36 36 1362 4231 FO 36 36 1351 4240 FO 36 36 1313 4296 FO 36 36 1268 4301 FO 36 36 1205 4379 FO 36 36 1172 4393 FO 36 36 1139 4423 FO 36 36 1115 4442 FO 36 36 1092 4462 FO 36 36 1067 4476 FO 36 36 1047 4495 FO 36 36 1024 4514 FO 36 36 1011 4523 FO 36 36 1003 4530 FO 36 36 1001 4536 FO 36 36 1001 4530 FO 36 36 1001 4531 FO 36 36 1001 4532 FO 36 36 984 4545 FO 36 36 977 4551 FO 36 36 974 4550 FO 36 36 969 4557 FO 36 36 969 4560 FO 36 36 968 4561 FO 36 36 963 4565 FO 36 36 962 4564 FO 36 36 956 4567 FO 36 36 955 4569 FO 36 36 954 4569 FO gs 898 388 5357 4226 MR c np gr 36 36 6052 552 FO 36 36 5499 1078 FO 36 36 4124 2140 FO 36 36 3626 2425 FO 36 36 3440 2466 FO 36 36 3284 2696 FO 36 36 2127 3598 FO 36 36 2117 3642 FO 36 36 2113 3604 FO 36 36 2072 3654 FO 36 36 1814 3893 FO 36 36 1811 3860 FO 36 36 1707 3929 FO 36 36 1599 4078 FO 36 36 1591 4042 FO 36 36 1504 4121 FO 36 36 1491 4125 FO 36 36 1481 4146 FO 36 36 1462 4152 FO 36 36 1254 4334 FO 36 36 1247 4325 FO 36 36 1152 4406 FO 36 36 1141 4422 FO 36 36 1128 4425 FO 36 36 1100 4452 FO 36 36 1068 4486 FO 36 36 1025 4513 FO 36 36 1008 4524 FO 36 36 1003 4530 FO 36 36 1001 4531 FO 36 36 991 4539 FO 36 36 991 4538 FO 36 36 990 4541 FO 36 36 984 4545 FO 36 36 982 4547 FO 36 36 969 4557 FO 36 36 964 4559 FO 36 36 963 4559 FO 36 36 955 4566 FO 36 36 947 4573 FO 36 36 940 4580 FO 36 36 935 4583 FO 36 36 933 4585 FO 36 36 933 4586 FO 36 36 931 4587 FO 36 36 931 4584 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6106 505 FO 36 36 5694 927 FO 36 36 3667 2468 FO 36 36 3423 2591 FO 36 36 2321 3542 FO 36 36 2200 3567 FO 36 36 2157 3555 FO 36 36 2135 3660 FO 36 36 2104 3692 FO 36 36 2012 3793 FO 36 36 1772 3959 FO 36 36 1668 3991 FO 36 36 1632 4003 FO 36 36 1424 4165 FO 36 36 1393 4230 FO 36 36 1221 4348 FO 36 36 1213 4381 FO 36 36 1208 4371 FO 36 36 1172 4398 FO 36 36 1170 4400 FO 36 36 1167 4408 FO 36 36 1143 4426 FO 36 36 1140 4430 FO 36 36 1091 4470 FO 36 36 1082 4475 FO 36 36 1072 4472 FO 36 36 1072 4478 FO 36 36 1064 4483 FO 36 36 1055 4490 FO 36 36 1048 4495 FO 36 36 1044 4504 FO 36 36 1038 4501 FO 36 36 1027 4510 FO 36 36 1023 4518 FO 36 36 1023 4514 FO 36 36 1014 4525 FO 36 36 1004 4535 FO 36 36 1001 4532 FO 36 36 1000 4532 FO 36 36 996 4535 FO 36 36 994 4539 FO 36 36 992 4539 FO 36 36 990 4540 FO 36 36 989 4541 FO 36 36 988 4545 FO 36 36 984 4547 FO 36 36 983 4549 FO 36 36 982 4549 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6252 388 FO 36 36 3607 2389 FO 36 36 3331 2645 FO 36 36 3266 2941 FO 36 36 3124 2810 FO 36 36 3078 2939 FO 36 36 3059 3065 FO 36 36 2862 3217 FO 36 36 2486 3471 FO 36 36 2327 3349 FO 36 36 2127 3655 FO 36 36 1994 3644 FO 36 36 1951 3795 FO 36 36 1642 4176 FO 36 36 1562 4092 FO 36 36 1474 4225 FO 36 36 1408 4254 FO 36 36 1371 4240 FO 36 36 1366 4260 FO 36 36 1325 4309 FO 36 36 1324 4213 FO 36 36 1289 4321 FO 36 36 1268 4327 FO 36 36 1258 4330 FO 36 36 1201 4426 FO 36 36 1179 4410 FO 36 36 1151 4424 FO 36 36 1139 4425 FO 36 36 1134 4446 FO 36 36 1126 4430 FO 36 36 1118 4434 FO 36 36 1106 4426 FO 36 36 1098 4453 FO 36 36 1090 4458 FO 36 36 1086 4488 FO 36 36 1070 4475 FO 36 36 1067 4494 FO 36 36 1056 4492 FO 36 36 1042 4503 FO 36 36 1036 4515 FO 36 36 1031 4509 FO 36 36 1029 4529 FO 36 36 1022 4498 FO 36 36 1017 4514 FO 36 36 1016 4547 FO 36 36 1010 4534 FO 36 36 1007 4527 FO 36 36 1006 4514 FO 36 36 998 4549 FO gs 898 388 5357 4226 MR c np gr 36 36 6000 587 FO 36 36 5749 767 FO 36 36 5160 1192 FO 36 36 3647 2512 FO 36 36 3563 2324 FO 36 36 3378 2573 FO 36 36 3160 2730 FO 36 36 2918 3074 FO 36 36 2650 3217 FO 36 36 1899 3853 FO 36 36 1574 4080 FO 36 36 1499 4224 FO 36 36 1290 4292 FO 36 36 1189 4376 FO 36 36 1133 4423 FO 36 36 1128 4425 FO 36 36 1108 4449 FO 36 36 1105 4448 FO 36 36 1077 4471 FO 36 36 1076 4472 FO 36 36 1058 4493 FO 36 36 1049 4493 FO 36 36 1049 4494 FO 36 36 1036 4504 FO 36 36 1018 4516 FO 36 36 1014 4518 FO 36 36 1008 4520 FO 36 36 1003 4539 FO 36 36 1001 4531 FO 36 36 1000 4531 FO 36 36 992 4539 FO 36 36 987 4540 FO 36 36 986 4542 FO 36 36 986 4544 FO 36 36 980 4546 FO 36 36 978 4551 FO 36 36 974 4552 FO 36 36 972 4556 FO 36 36 970 4556 FO 36 36 961 4564 FO 36 36 960 4565 FO 36 36 960 4566 FO 36 36 956 4572 FO 36 36 953 4570 FO 36 36 953 4571 FO 36 36 950 4572 FO 36 36 947 4576 FO 36 36 947 4574 FO 36 36 946 4574 FO 36 36 944 4575 FO gs 898 388 5357 4226 MR c np gr 36 36 3545 2590 FO 36 36 3355 2640 FO 36 36 3081 2859 FO 36 36 3028 2983 FO 36 36 2895 3009 FO 36 36 2526 3316 FO 36 36 2247 3574 FO 36 36 2226 3604 FO 36 36 2183 3596 FO 36 36 1752 3903 FO 36 36 1689 3986 FO 36 36 1481 4158 FO 36 36 1469 4158 FO 36 36 1397 4223 FO 36 36 1386 4231 FO 36 36 1375 4236 FO 36 36 1368 4243 FO 36 36 1286 4309 FO 36 36 1222 4362 FO 36 36 1180 4390 FO 36 36 1168 4402 FO 36 36 1162 4404 FO 36 36 1159 4403 FO 36 36 1158 4408 FO 36 36 1083 4456 FO 36 36 1068 4480 FO 36 36 1046 4498 FO 36 36 1046 4501 FO 36 36 1044 4500 FO 36 36 1041 4500 FO 36 36 1040 4496 FO 36 36 1030 4518 FO 36 36 1025 4510 FO 36 36 1018 4521 FO 36 36 1015 4521 FO 36 36 1013 4529 FO 36 36 1012 4525 FO 36 36 1009 4523 FO 36 36 1008 4528 FO 36 36 1005 4528 FO 36 36 1002 4531 FO 36 36 1002 4531 FO 36 36 998 4535 FO 36 36 991 4539 FO 36 36 990 4539 FO 36 36 988 4542 FO 36 36 987 4543 FO 36 36 986 4545 FO 36 36 981 4549 FO 36 36 978 4551 FO gs 898 388 5357 4226 MR c np gr 36 36 5478 1010 FO 36 36 3328 2691 FO 36 36 2731 3184 FO 36 36 2612 3263 FO 36 36 1808 3906 FO 36 36 1576 4085 FO 36 36 1335 4270 FO 36 36 1267 4321 FO 36 36 1221 4357 FO 36 36 1175 4394 FO 36 36 1140 4423 FO 36 36 1120 4438 FO 36 36 1106 4449 FO 36 36 1065 4482 FO 36 36 1060 4486 FO 36 36 1059 4486 FO 36 36 1057 4488 FO 36 36 1047 4495 FO 36 36 1046 4496 FO 36 36 1039 4501 FO 36 36 1038 4503 FO 36 36 1038 4503 FO 36 36 1034 4506 FO 36 36 1031 4507 FO 36 36 1024 4514 FO 36 36 1024 4514 FO 36 36 1020 4518 FO 36 36 1013 4524 FO 36 36 1013 4523 FO 36 36 1008 4526 FO 36 36 1007 4527 FO 36 36 1003 4529 FO 36 36 1001 4531 FO 36 36 1000 4532 FO 36 36 1000 4534 FO 36 36 995 4537 FO 36 36 986 4543 FO 36 36 985 4545 FO 36 36 982 4547 FO 36 36 980 4549 FO 36 36 978 4550 FO 36 36 977 4550 FO 36 36 973 4553 FO 36 36 971 4556 FO 36 36 966 4560 FO 36 36 964 4561 FO 36 36 963 4561 FO 36 36 956 4567 FO gs 898 388 5357 4226 MR c np gr 36 36 6252 389 FO 36 36 5327 1119 FO 36 36 2468 3358 FO 36 36 2006 3755 FO 36 36 1779 3918 FO 36 36 1688 3975 FO 36 36 1617 4051 FO 36 36 1365 4244 FO 36 36 1283 4307 FO 36 36 1265 4323 FO 36 36 1265 4327 FO 36 36 1182 4391 FO 36 36 1154 4413 FO 36 36 1121 4431 FO 36 36 1093 4455 FO 36 36 1039 4498 FO 36 36 1039 4503 FO 36 36 1010 4524 FO 36 36 1007 4527 FO 36 36 998 4536 FO 36 36 990 4541 FO 36 36 975 4553 FO 36 36 974 4554 FO 36 36 969 4557 FO 36 36 962 4563 FO 36 36 960 4564 FO 36 36 960 4562 FO 36 36 959 4565 FO 36 36 950 4572 FO 36 36 948 4574 FO 36 36 946 4575 FO 36 36 945 4576 FO 36 36 943 4578 FO 36 36 942 4578 FO 36 36 939 4580 FO 36 36 936 4582 FO 36 36 935 4583 FO 36 36 934 4585 FO 36 36 934 4584 FO 36 36 933 4585 FO 36 36 933 4584 FO 36 36 932 4586 FO 36 36 928 4589 FO 36 36 927 4590 FO 36 36 926 4591 FO 36 36 925 4592 FO 36 36 924 4592 FO 36 36 923 4593 FO gs 898 388 5357 4226 MR c np gr 36 36 5432 1020 FO 36 36 4383 1844 FO 36 36 3957 2184 FO 36 36 2678 3199 FO 36 36 2674 3226 FO 36 36 2285 3501 FO 36 36 1840 3846 FO 36 36 1399 4188 FO 36 36 1369 4242 FO 36 36 1339 4256 FO 36 36 1259 4331 FO 36 36 1199 4375 FO 36 36 1157 4407 FO 36 36 1144 4414 FO 36 36 1129 4429 FO 36 36 1091 4454 FO 36 36 1067 4479 FO 36 36 1059 4486 FO 36 36 1034 4506 FO 36 36 1030 4509 FO 36 36 1009 4526 FO 36 36 1008 4526 FO 36 36 1001 4531 FO 36 36 997 4535 FO 36 36 992 4539 FO 36 36 985 4543 FO 36 36 982 4547 FO 36 36 981 4548 FO 36 36 972 4553 FO 36 36 971 4555 FO 36 36 969 4557 FO 36 36 969 4556 FO 36 36 968 4557 FO 36 36 968 4557 FO 36 36 967 4558 FO 36 36 966 4557 FO 36 36 964 4560 FO 36 36 957 4566 FO 36 36 955 4567 FO 36 36 953 4569 FO 36 36 945 4575 FO 36 36 944 4577 FO 36 36 940 4580 FO 36 36 937 4583 FO 36 36 936 4583 FO 36 36 934 4585 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6249 395 FO 36 36 6114 511 FO 36 36 5841 718 FO 36 36 5204 1233 FO 36 36 3345 2669 FO 36 36 2016 3726 FO 36 36 1991 3763 FO 36 36 1373 4244 FO 36 36 1365 4245 FO 36 36 1278 4319 FO 36 36 1277 4317 FO 36 36 1208 4367 FO 36 36 1174 4394 FO 36 36 1170 4400 FO 36 36 1097 4456 FO 36 36 1052 4490 FO 36 36 1052 4493 FO 36 36 1047 4495 FO 36 36 1037 4504 FO 36 36 1026 4512 FO 36 36 1021 4516 FO 36 36 1020 4518 FO 36 36 1020 4517 FO 36 36 1002 4531 FO 36 36 999 4535 FO 36 36 998 4534 FO 36 36 998 4534 FO 36 36 996 4536 FO 36 36 994 4537 FO 36 36 994 4537 FO 36 36 992 4539 FO 36 36 989 4541 FO 36 36 989 4542 FO 36 36 986 4543 FO 36 36 983 4544 FO 36 36 982 4548 FO 36 36 978 4550 FO 36 36 977 4551 FO 36 36 971 4557 FO 36 36 968 4561 FO 36 36 963 4560 FO 36 36 959 4565 FO 36 36 958 4565 FO 36 36 958 4567 FO 36 36 957 4566 FO 36 36 955 4567 FO 36 36 954 4569 FO gs 898 388 5357 4226 MR c np gr 36 36 5950 582 FO 36 36 5168 1278 FO 36 36 4007 2108 FO 36 36 3851 2242 FO 36 36 3827 2273 FO 36 36 3650 2408 FO 36 36 2872 3055 FO 36 36 2534 3250 FO 36 36 1486 4139 FO 36 36 1439 4190 FO 36 36 1335 4259 FO 36 36 1319 4270 FO 36 36 1269 4316 FO 36 36 1222 4351 FO 36 36 1207 4371 FO 36 36 1179 4393 FO 36 36 1170 4403 FO 36 36 1168 4381 FO 36 36 1166 4406 FO 36 36 1162 4406 FO 36 36 1160 4381 FO 36 36 1150 4425 FO 36 36 1142 4419 FO 36 36 1140 4418 FO 36 36 1125 4436 FO 36 36 1121 4437 FO 36 36 1103 4461 FO 36 36 1092 4459 FO 36 36 1064 4478 FO 36 36 1062 4484 FO 36 36 1061 4483 FO 36 36 1061 4479 FO 36 36 1052 4492 FO 36 36 1052 4474 FO 36 36 1042 4504 FO 36 36 1042 4498 FO 36 36 1020 4519 FO 36 36 1020 4516 FO 36 36 1019 4555 FO 36 36 1015 4526 FO 36 36 1013 4521 FO 36 36 1007 4527 FO 36 36 1002 4531 FO 36 36 994 4539 FO 36 36 992 4538 FO 36 36 990 4540 FO 36 36 989 4547 FO 36 36 985 4544 FO 36 36 984 4544 FO 36 36 982 4547 FO gs 898 388 5357 4226 MR c np gr 36 36 5771 777 FO 36 36 5350 1169 FO 36 36 5309 1111 FO 36 36 3517 2612 FO 36 36 3485 2536 FO 36 36 3451 2538 FO 36 36 3382 2550 FO 36 36 2567 3257 FO 36 36 1571 4074 FO 36 36 1499 4095 FO 36 36 1466 4152 FO 36 36 1371 4199 FO 36 36 1341 4261 FO 36 36 1316 4294 FO 36 36 1283 4277 FO 36 36 1261 4313 FO 36 36 1248 4340 FO 36 36 1236 4366 FO 36 36 1167 4397 FO 36 36 1120 4430 FO 36 36 1119 4439 FO 36 36 1118 4428 FO 36 36 1115 4438 FO 36 36 1104 4445 FO 36 36 1098 4449 FO 36 36 1092 4455 FO 36 36 1077 4467 FO 36 36 1068 4482 FO 36 36 1067 4475 FO 36 36 1055 4483 FO 36 36 1051 4493 FO 36 36 1046 4502 FO 36 36 1044 4496 FO 36 36 1038 4505 FO 36 36 1027 4517 FO 36 36 1024 4512 FO 36 36 1018 4509 FO 36 36 1017 4510 FO 36 36 1007 4524 FO 36 36 1005 4528 FO 36 36 1005 4525 FO 36 36 1004 4529 FO 36 36 1000 4529 FO 36 36 1000 4527 FO 36 36 997 4534 FO 36 36 994 4537 FO 36 36 987 4540 FO 36 36 983 4542 FO 36 36 979 4546 FO 36 36 979 4547 FO gs 898 388 5357 4226 MR c np gr 36 36 6251 403 FO 36 36 6085 445 FO 36 36 5134 933 FO 36 36 4863 1136 FO 36 36 3838 2178 FO 36 36 3552 1724 FO 36 36 3396 2304 FO 36 36 2509 3364 FO 36 36 2226 3381 FO 36 36 2039 4236 FO 36 36 1872 4257 FO 36 36 1865 3620 FO 36 36 1849 3374 FO 36 36 1627 4262 FO 36 36 1461 4441 FO 36 36 1425 4385 FO 36 36 1221 4484 FO 36 36 1206 4392 FO 36 36 1170 4521 FO 36 36 1156 4525 FO 36 36 1138 4495 FO 36 36 1132 4483 FO 36 36 1129 4477 FO 36 36 1129 4500 FO 36 36 1125 4433 FO 36 36 1117 4484 FO 36 36 1097 4529 FO 36 36 1096 4529 FO 36 36 1096 4538 FO 36 36 1088 4549 FO 36 36 1087 4545 FO 36 36 1086 4520 FO 36 36 1081 4554 FO 36 36 1081 4511 FO 36 36 1074 4548 FO 36 36 1068 4497 FO 36 36 1065 4541 FO 36 36 1065 4510 FO 36 36 1046 4509 FO 36 36 1045 4488 FO 36 36 1042 4494 FO 36 36 1036 4500 FO 36 36 1034 4532 FO 36 36 1031 4463 FO 36 36 1012 4570 FO 36 36 1010 4559 FO 36 36 1009 4523 FO 36 36 1008 4529 FO 36 36 1004 4579 FO 36 36 1001 4569 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 6061 527 FO 36 36 5578 884 FO 36 36 5250 1263 FO 36 36 4247 1998 FO 36 36 4193 2027 FO 36 36 3870 2324 FO 36 36 3506 2630 FO 36 36 2897 3095 FO 36 36 2630 3233 FO 36 36 2476 3271 FO 36 36 2264 3527 FO 36 36 1917 3788 FO 36 36 1789 3877 FO 36 36 1700 3962 FO 36 36 1634 4033 FO 36 36 1618 4084 FO 36 36 1517 4136 FO 36 36 1507 4139 FO 36 36 1488 4122 FO 36 36 1485 4151 FO 36 36 1431 4210 FO 36 36 1348 4267 FO 36 36 1344 4250 FO 36 36 1321 4279 FO 36 36 1295 4298 FO 36 36 1294 4302 FO 36 36 1255 4329 FO 36 36 1229 4321 FO 36 36 1198 4368 FO 36 36 1193 4385 FO 36 36 1150 4413 FO 36 36 1126 4436 FO 36 36 1119 4436 FO 36 36 1119 4428 FO 36 36 1113 4447 FO 36 36 1098 4454 FO 36 36 1098 4444 FO 36 36 1093 4458 FO 36 36 1090 4460 FO 36 36 1083 4458 FO 36 36 1078 4476 FO 36 36 1066 4474 FO 36 36 1062 4476 FO 36 36 1059 4494 FO 36 36 1056 4498 FO 36 36 1054 4491 FO 36 36 1054 4489 FO 36 36 1044 4498 FO 36 36 1024 4516 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 4630 1713 FO 36 36 3645 2473 FO 36 36 2467 3375 FO 36 36 2246 3535 FO 36 36 1592 4081 FO 36 36 1487 4156 FO 36 36 1440 4186 FO 36 36 1264 4337 FO 36 36 1213 4365 FO 36 36 1212 4362 FO 36 36 1172 4397 FO 36 36 1140 4428 FO 36 36 1138 4424 FO 36 36 1137 4431 FO 36 36 1106 4449 FO 36 36 1100 4460 FO 36 36 1094 4459 FO 36 36 1088 4471 FO 36 36 1084 4466 FO 36 36 1084 4467 FO 36 36 1070 4479 FO 36 36 1046 4500 FO 36 36 1037 4503 FO 36 36 1020 4517 FO 36 36 1016 4522 FO 36 36 1015 4523 FO 36 36 1014 4522 FO 36 36 1012 4523 FO 36 36 1011 4524 FO 36 36 1009 4526 FO 36 36 1009 4526 FO 36 36 990 4543 FO 36 36 985 4545 FO 36 36 971 4556 FO 36 36 963 4562 FO 36 36 958 4568 FO 36 36 958 4567 FO 36 36 957 4567 FO 36 36 956 4567 FO 36 36 954 4569 FO 36 36 953 4569 FO 36 36 953 4572 FO 36 36 953 4570 FO 36 36 952 4571 FO 36 36 950 4572 FO 36 36 949 4572 FO 36 36 948 4575 FO 36 36 947 4575 FO gs 898 388 5357 4226 MR c np gr 36 36 6254 388 FO 36 36 5853 705 FO 36 36 5747 812 FO 36 36 4869 1553 FO 36 36 3160 2833 FO 36 36 3096 2856 FO 36 36 2990 2929 FO 36 36 2798 3126 FO 36 36 1870 3864 FO 36 36 1849 3865 FO 36 36 1834 3898 FO 36 36 1654 4012 FO 36 36 1593 4068 FO 36 36 1501 4156 FO 36 36 1356 4264 FO 36 36 1350 4249 FO 36 36 1258 4327 FO 36 36 1173 4409 FO 36 36 1166 4403 FO 36 36 1157 4404 FO 36 36 1120 4438 FO 36 36 1112 4441 FO 36 36 1092 4453 FO 36 36 1050 4493 FO 36 36 1044 4499 FO 36 36 1041 4500 FO 36 36 1039 4501 FO 36 36 1029 4509 FO 36 36 1026 4503 FO 36 36 1022 4519 FO 36 36 1019 4512 FO 36 36 1016 4520 FO 36 36 1013 4520 FO 36 36 1011 4522 FO 36 36 1007 4525 FO 36 36 1002 4531 FO 36 36 1001 4532 FO 36 36 994 4537 FO 36 36 993 4539 FO 36 36 993 4539 FO 36 36 992 4542 FO 36 36 977 4551 FO 36 36 975 4556 FO 36 36 972 4555 FO 36 36 971 4556 FO 36 36 970 4555 FO 36 36 967 4559 FO 36 36 965 4560 FO 36 36 963 4563 FO 36 36 962 4563 FO gs 898 388 5357 4226 MR c np gr 36 36 5461 1119 FO 36 36 4897 1421 FO 36 36 4485 1827 FO 36 36 3992 2201 FO 36 36 3382 2633 FO 36 36 3084 2858 FO 36 36 2762 3176 FO 36 36 2519 3354 FO 36 36 2473 3315 FO 36 36 1853 3863 FO 36 36 1505 4175 FO 36 36 1411 4230 FO 36 36 1408 4243 FO 36 36 1405 4237 FO 36 36 1325 4285 FO 36 36 1236 4370 FO 36 36 1215 4372 FO 36 36 1163 4400 FO 36 36 1144 4422 FO 36 36 1129 4433 FO 36 36 1101 4451 FO 36 36 1085 4485 FO 36 36 1084 4465 FO 36 36 1066 4466 FO 36 36 1061 4500 FO 36 36 1049 4494 FO 36 36 1041 4499 FO 36 36 1032 4509 FO 36 36 1031 4507 FO 36 36 1031 4509 FO 36 36 1027 4520 FO 36 36 1024 4513 FO 36 36 1005 4529 FO 36 36 1005 4527 FO 36 36 1002 4531 FO 36 36 1001 4531 FO 36 36 999 4532 FO 36 36 997 4535 FO 36 36 994 4547 FO 36 36 994 4544 FO 36 36 984 4545 FO 36 36 979 4554 FO 36 36 978 4553 FO 36 36 972 4554 FO 36 36 972 4560 FO 36 36 969 4553 FO 36 36 962 4565 FO 36 36 960 4563 FO 36 36 960 4564 FO gs 898 388 5357 4226 MR c np gr 2563 5063 mt (sampling estimates 1) s 508 3514 mt -90 rotate (sampling estimates 2) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 710 a Fm(Figure)e(10:)22 b(A)c(correlation)g(plot)f(b)q(et)o(w)o (een)h(the)g(selected)h(p)q(osterior)e(marginal)h(estimates)f(from)g(t) o(w)o(o)299 766 y(indep)q(enden)o(t)23 b(sampling)e(runs,)g(where)g (the)f(selection)i(w)o(as)d(based)i(on)f(the)g(v)m(ariational)299 823 y(upp)q(er)c(and)g(lo)o(w)o(er)f(b)q(ounds.)652 933 y 10194856 8288501 3157524 12169625 36377313 39008583 startTexFig 652 933 a %%BeginDocument: figures/all-12-s8.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 362 217 6061 4896 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5186 PR 6 w 0 4225 5356 0 0 -4225 898 4613 4 MP PP -5356 0 0 4225 5356 0 0 -4225 898 4613 5 MP stroke 4 w DO SO 6 w 0 sg 898 4613 mt 6254 4613 L 898 388 mt 6254 388 L 6254 4613 mt 6254 388 L 898 4613 mt 898 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 898 4613 mt 898 4559 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4849 mt (0) s 1969 4613 mt 1969 4559 L 1969 388 mt 1969 442 L 1849 4849 mt (10) s 3040 4613 mt 3040 4559 L 3040 388 mt 3040 442 L 2920 4849 mt (20) s 4112 4613 mt 4112 4559 L 4112 388 mt 4112 442 L 3992 4849 mt (30) s 5183 4613 mt 5183 4559 L 5183 388 mt 5183 442 L 5063 4849 mt (40) s 6254 4613 mt 6254 4559 L 6254 388 mt 6254 442 L 6134 4849 mt (50) s 898 4613 mt 952 4613 L 6254 4613 mt 6200 4613 L 743 4693 mt (0) s 898 4009 mt 952 4009 L 6254 4009 mt 6200 4009 L 623 4089 mt (10) s 898 3406 mt 952 3406 L 6254 3406 mt 6200 3406 L 623 3486 mt (20) s 898 2802 mt 952 2802 L 6254 2802 mt 6200 2802 L 623 2882 mt (30) s 898 2199 mt 952 2199 L 6254 2199 mt 6200 2199 L 623 2279 mt (40) s 898 1595 mt 952 1595 L 6254 1595 mt 6200 1595 L 623 1675 mt (50) s 898 992 mt 952 992 L 6254 992 mt 6200 992 L 623 1072 mt (60) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 623 468 mt (70) s 898 388 mt 6254 388 L 898 4613 mt 6254 4613 L 898 4613 mt 898 388 L 6254 4613 mt 6254 388 L gs 898 388 5357 4226 MR c np 107 -29 107 -22 107 46 107 24 108 -26 107 0 107 7 107 19 107 51 107 -7 107 -77 107 -3 108 -67 107 24 107 -116 107 -104 107 15 107 -37 107 -89 107 24 108 -31 107 38 107 -84 107 5 107 -63 107 -176 107 -44 107 20 107 -29 108 -83 107 -111 107 -55 107 19 107 12 107 0 107 -63 107 -14 108 -48 107 -51 107 -7 107 -119 107 8 107 -36 107 -37 107 -5 108 -26 107 -17 107 -46 107 -17 1005 4606 50 MP stroke gr gs 932 3036 5396 1644 MR c np 36 36 1005 4606 FO 36 36 1112 4589 FO 36 36 1219 4543 FO 36 36 1326 4526 FO 36 36 1434 4500 FO 36 36 1541 4495 FO 36 36 1648 4458 FO 36 36 1755 4422 FO 36 36 1862 4430 FO 36 36 1969 4311 FO 36 36 2076 4304 FO 36 36 2183 4253 FO 36 36 2291 4205 FO 36 36 2398 4191 FO 36 36 2505 4128 FO 36 36 2612 4128 FO 36 36 2719 4140 FO 36 36 2826 4159 FO 36 36 2933 4104 FO 36 36 3040 3993 FO 36 36 3148 3910 FO 36 36 3255 3881 FO 36 36 3362 3901 FO 36 36 3469 3857 FO 36 36 3576 3681 FO 36 36 3683 3618 FO 36 36 3790 3623 FO 36 36 3897 3539 FO 36 36 4004 3577 FO 36 36 4112 3546 FO 36 36 4219 3570 FO 36 36 4326 3481 FO 36 36 4433 3444 FO 36 36 4540 3459 FO 36 36 4647 3355 FO 36 36 4754 3239 FO 36 36 4861 3263 FO 36 36 4969 3196 FO 36 36 5076 3193 FO 36 36 5183 3116 FO 36 36 5290 3109 FO 36 36 5397 3160 FO 36 36 5504 3179 FO 36 36 5611 3186 FO 36 36 5718 3186 FO 36 36 5826 3160 FO 36 36 5933 3184 FO 36 36 6040 3230 FO 36 36 6147 3208 FO 36 36 6254 3179 FO gr gs 898 388 5357 4226 MR c np DA 107 -21 107 1 107 -8 107 6 108 -43 107 15 107 -71 107 -8 107 -7 107 -67 107 9 107 -7 108 -26 107 -20 107 -44 107 10 107 -12 107 -22 107 -55 107 -32 108 -91 107 -64 107 -54 107 -25 107 -56 107 -56 107 -57 107 -26 107 -94 108 -118 107 -105 107 -41 107 -176 107 -251 107 -89 107 -51 107 -130 108 -150 107 -205 107 -232 107 -105 107 -63 107 -138 107 -35 107 -125 108 -191 107 -395 107 -282 107 -190 1005 4536 50 MP stroke SO gr gs 932 466 5396 4144 MR c np 980 4511 mt 1030 4561 L 1030 4511 mt 980 4561 L 1087 4321 mt 1137 4371 L 1137 4321 mt 1087 4371 L 1194 4039 mt 1244 4089 L 1244 4039 mt 1194 4089 L 1301 3644 mt 1351 3694 L 1351 3644 mt 1301 3694 L 1409 3453 mt 1459 3503 L 1459 3453 mt 1409 3503 L 1516 3328 mt 1566 3378 L 1566 3328 mt 1516 3378 L 1623 3293 mt 1673 3343 L 1673 3293 mt 1623 3343 L 1730 3155 mt 1780 3205 L 1780 3155 mt 1730 3205 L 1837 3092 mt 1887 3142 L 1887 3092 mt 1837 3142 L 1944 2987 mt 1994 3037 L 1994 2987 mt 1944 3037 L 2051 2755 mt 2101 2805 L 2101 2755 mt 2051 2805 L 2158 2550 mt 2208 2600 L 2208 2550 mt 2158 2600 L 2266 2400 mt 2316 2450 L 2316 2400 mt 2266 2450 L 2373 2270 mt 2423 2320 L 2423 2270 mt 2373 2320 L 2480 2219 mt 2530 2269 L 2530 2219 mt 2480 2269 L 2587 2130 mt 2637 2180 L 2637 2130 mt 2587 2180 L 2694 1879 mt 2744 1929 L 2744 1879 mt 2694 1929 L 2801 1703 mt 2851 1753 L 2851 1703 mt 2801 1753 L 2908 1662 mt 2958 1712 L 2958 1662 mt 2908 1712 L 3015 1557 mt 3065 1607 L 3065 1557 mt 3015 1607 L 3123 1439 mt 3173 1489 L 3173 1439 mt 3123 1489 L 3230 1345 mt 3280 1395 L 3280 1345 mt 3230 1395 L 3337 1319 mt 3387 1369 L 3387 1319 mt 3337 1369 L 3444 1262 mt 3494 1312 L 3494 1262 mt 3444 1312 L 3551 1206 mt 3601 1256 L 3601 1206 mt 3551 1256 L 3658 1150 mt 3708 1200 L 3708 1150 mt 3658 1200 L 3765 1125 mt 3815 1175 L 3815 1125 mt 3765 1175 L 3872 1071 mt 3922 1121 L 3922 1071 mt 3872 1121 L 3979 1007 mt 4029 1057 L 4029 1007 mt 3979 1057 L 4087 916 mt 4137 966 L 4137 916 mt 4087 966 L 4194 884 mt 4244 934 L 4244 884 mt 4194 934 L 4301 829 mt 4351 879 L 4351 829 mt 4301 879 L 4408 807 mt 4458 857 L 4458 807 mt 4408 857 L 4515 795 mt 4565 845 L 4565 795 mt 4515 845 L 4622 805 mt 4672 855 L 4672 805 mt 4622 855 L 4729 761 mt 4779 811 L 4779 761 mt 4729 811 L 4836 741 mt 4886 791 L 4886 741 mt 4836 791 L 4944 715 mt 4994 765 L 4994 715 mt 4944 765 L 5051 708 mt 5101 758 L 5101 708 mt 5051 758 L 5158 717 mt 5208 767 L 5208 717 mt 5158 767 L 5265 650 mt 5315 700 L 5315 650 mt 5265 700 L 5372 643 mt 5422 693 L 5422 643 mt 5372 693 L 5479 635 mt 5529 685 L 5529 635 mt 5479 685 L 5586 564 mt 5636 614 L 5636 564 mt 5586 614 L 5693 579 mt 5743 629 L 5743 579 mt 5693 629 L 5801 536 mt 5851 586 L 5851 536 mt 5801 586 L 5908 542 mt 5958 592 L 5958 542 mt 5908 592 L 6015 534 mt 6065 584 L 6065 534 mt 6015 584 L 6122 535 mt 6172 585 L 6172 535 mt 6122 585 L 6229 514 mt 6279 564 L 6279 514 mt 6229 564 L gr gs 898 388 5357 4226 MR c np gr 2910 5063 mt (true positives) s 568 3179 mt -90 rotate (false positives) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 1564 a Fm(Figure)g(11:)22 b(Av)o(erage)d(n)o(um)o(b)q(er)g(of)g (false)g(p)q(ositiv)o(es)h(as)f(a)g(function)h(of)f(true)g(p)q(ositiv)o 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(originate)g(from)e(upp)q(er)i(and)f(lo)o(w)o(er)954 2753 y Fn(21)p eop %%Page: 22 22 22 21 bop 759 -100 a Fq(Jaakk)o(ola)18 b(&)e(Jord)o(an)75 124 y Fm(b)q(ounds)g(on)f(the)h(lik)o(eliho)q(o)q(d,)h(but)f(they)f (are)g(not)g(themselv)o(es)g(b)q(ounds.)21 b(That)15 b(is,)g(they)h(are)f(not)f(guar-)75 181 y(an)o(teed)i(to)f(lie)i(ab)q (o)o(v)o(e)e(or)h(b)q(elo)o(w)g(the)g(true)f(p)q(osteriors,)h(as)f(w)o (e)h(see)g(in)g(Figure)g(4.)22 b(As)15 b(w)o(e)h(discussed)h(in)75 237 y(Section)f(4.1,)e(ho)o(w)o(ev)o(er,)g(it)i(is)g(also)f(p)q (ossible)i(to)e(induce)i(upp)q(er)g(and)e(lo)o(w)o(er)g(b)q(ounds)h(on) g(the)f(p)q(osterior)75 294 y(marginals)i(from)f(upp)q(er)i(and)f(lo)o (w)o(er)f(b)q(ounds)h(on)g(the)g(lik)o(eliho)q(o)q(d)j(\(cf.)k(Eq.)16 b(33\).)23 b(In)18 b(this)f(section)g(w)o(e)75 350 y(ev)m(aluate)f (these)f(in)o(terv)m(al)i(b)q(ounds)f(for)e(the)i(QMR-DT)f(p)q (osterior)g(marginals.)146 418 y(Figure)d(12)f(displa)o(ys)h(histogram) f(of)h(the)f(in)o(terv)m(al)i(b)q(ounds)g(for)e(the)h(four)f(tractable) h(CPC)f(cases,)h(the)75 474 y(24)e(selected)j(CPC)d(cases)h(from)g(the) g(previous)g(section,)h(and)g(all)g(of)e(the)h(CPC)g(cases.)18 b(These)12 b(histograms)75 531 y(include)19 b(all)e(of)f(the)g (diseases)h(in)g(the)f(QMR-DT)h(net)o(w)o(ork.)22 b(In)17 b(the)f(case)g(of)g(the)h(tractable)f(cases)g(the)-5 1020 y(\(a\))68 612 y 8051672 6441336 2368143 11840716 35982622 39008583 startTexFig 68 612 a %%BeginDocument: figures/ul-16-exact.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0204 7344 csm 235 217 6128 4964 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w 0 4224 5356 0 0 -4224 898 4612 4 MP PP -5356 0 0 4224 5356 0 0 -4224 898 4612 5 MP stroke 4 w DO SO 6 w 0 sg 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L 898 4612 mt 6254 4612 L 898 4612 mt 898 388 L 898 4612 mt 898 4558 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4848 mt (0) s 1969 4612 mt 1969 4558 L 1969 388 mt 1969 442 L 1819 4848 mt (0.2) s 3040 4612 mt 3040 4558 L 3040 388 mt 3040 442 L 2890 4848 mt (0.4) s 4112 4612 mt 4112 4558 L 4112 388 mt 4112 442 L 3962 4848 mt (0.6) s 5183 4612 mt 5183 4558 L 5183 388 mt 5183 442 L 5033 4848 mt (0.8) s 6254 4612 mt 6254 4558 L 6254 388 mt 6254 442 L 6194 4848 mt (1) s 898 4612 mt 952 4612 L 6254 4612 mt 6200 4612 L 743 4692 mt (0) s 898 3767 mt 952 3767 L 6254 3767 mt 6200 3767 L 563 3847 mt (0.2) s 898 2922 mt 952 2922 L 6254 2922 mt 6200 2922 L 563 3002 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L gs 898 388 5357 4225 MR c np /c8 { 0.000000 0.000000 0.562500 sr} bdef c8 0 4010 171 0 0 -4010 919 4612 4 MP PP 0 sg -171 0 0 4010 171 0 0 -4010 919 4612 5 MP stroke c8 0 92 171 0 0 -92 1133 4612 4 MP PP 0 sg -171 0 0 92 171 0 0 -92 1133 4612 5 MP stroke c8 0 22 171 0 0 -22 1346 4612 4 MP PP 0 sg -171 0 0 22 171 0 0 -22 1346 4612 5 MP stroke c8 0 17 170 0 0 -17 1560 4612 4 MP PP 0 sg -170 0 0 17 170 0 0 -17 1560 4612 5 MP stroke c8 0 11 171 0 0 -11 1773 4612 4 MP PP 0 sg -171 0 0 11 171 0 0 -11 1773 4612 5 MP stroke c8 0 7 170 0 0 -7 1987 4612 4 MP PP 0 sg -170 0 0 7 170 0 0 -7 1987 4612 5 MP stroke c8 0 4 171 0 0 -4 2200 4612 4 MP PP 0 sg -171 0 0 4 171 0 0 -4 2200 4612 5 MP stroke c8 0 9 170 0 0 -9 2414 4612 4 MP PP 0 sg -170 0 0 9 170 0 0 -9 2414 4612 5 MP stroke c8 0 6 171 0 0 -6 2627 4612 4 MP PP 0 sg -171 0 0 6 171 0 0 -6 2627 4612 5 MP stroke c8 0 6 171 0 0 -6 2840 4612 4 MP PP 0 sg -171 0 0 6 171 0 0 -6 2840 4612 5 MP stroke c8 0 2 171 0 0 -2 3054 4612 4 MP PP 0 sg -171 0 0 2 171 0 0 -2 3054 4612 5 MP stroke c8 0 6 171 0 0 -6 3267 4612 4 MP PP 0 sg -171 0 0 6 171 0 0 -6 3267 4612 5 MP stroke c8 0 7 171 0 0 -7 3481 4612 4 MP PP 0 sg -171 0 0 7 171 0 0 -7 3481 4612 5 MP stroke c8 0 4 171 0 0 -4 3694 4612 4 MP PP 0 sg -171 0 0 4 171 0 0 -4 3694 4612 5 MP stroke c8 0 6 171 0 0 -6 3908 4612 4 MP PP 0 sg -171 0 0 6 171 0 0 -6 3908 4612 5 MP stroke c8 0 4 171 0 0 -4 4121 4612 4 MP PP 0 sg -171 0 0 4 171 0 0 -4 4121 4612 5 MP stroke c8 0 2 170 0 0 -2 4335 4612 4 MP PP 0 sg -170 0 0 2 170 0 0 -2 4335 4612 5 MP stroke c8 0 4 171 0 0 -4 4548 4612 4 MP PP 0 sg -171 0 0 4 171 0 0 -4 4548 4612 5 MP stroke c8 0 0 170 0 0 0 4762 4612 4 MP PP 0 sg -170 0 0 0 170 0 0 0 4762 4612 5 MP stroke c8 0 7 171 0 0 -7 4975 4612 4 MP PP 0 sg -171 0 0 7 171 0 0 -7 4975 4612 5 MP stroke gr /Helvetica /ISOLatin1Encoding 288 FMSR 2808 5115 mt (Interval size) s 508 3180 mt -90 rotate (Frequency) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 658 1020 a Fm(\(b\))734 612 y 8051672 6441336 2368143 11840716 35982622 39008583 startTexFig 734 612 a %%BeginDocument: figures/ul-16-select.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0204 7344 csm 235 217 6128 4964 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w 0 4224 5356 0 0 -4224 898 4612 4 MP PP -5356 0 0 4224 5356 0 0 -4224 898 4612 5 MP stroke 4 w DO SO 6 w 0 sg 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L 898 4612 mt 6254 4612 L 898 4612 mt 898 388 L 898 4612 mt 898 4558 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4848 mt (0) s 1969 4612 mt 1969 4558 L 1969 388 mt 1969 442 L 1819 4848 mt (0.2) s 3040 4612 mt 3040 4558 L 3040 388 mt 3040 442 L 2890 4848 mt (0.4) s 4112 4612 mt 4112 4558 L 4112 388 mt 4112 442 L 3962 4848 mt (0.6) s 5183 4612 mt 5183 4558 L 5183 388 mt 5183 442 L 5033 4848 mt (0.8) s 6254 4612 mt 6254 4558 L 6254 388 mt 6254 442 L 6194 4848 mt (1) s 898 4612 mt 952 4612 L 6254 4612 mt 6200 4612 L 743 4692 mt (0) s 898 3767 mt 952 3767 L 6254 3767 mt 6200 3767 L 563 3847 mt (0.2) s 898 2922 mt 952 2922 L 6254 2922 mt 6200 2922 L 563 3002 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L gs 898 388 5357 4225 MR c np /c8 { 0.000000 0.000000 0.562500 sr} bdef c8 0 1 255 0 0 -1 -115 4612 4 MP PP 0 sg -255 0 0 1 255 0 0 -1 -115 4612 5 MP stroke c8 0 0 256 0 0 0 204 4612 4 MP PP 0 sg -256 0 0 0 256 0 0 0 204 4612 5 MP stroke c8 0 3 256 0 0 -3 524 4612 4 MP PP 0 sg -256 0 0 3 256 0 0 -3 524 4612 5 MP stroke c8 0 1976 256 0 0 -1976 844 4612 4 MP PP 0 sg -256 0 0 1976 256 0 0 -1976 844 4612 5 MP stroke c8 0 254 256 0 0 -254 1164 4612 4 MP PP 0 sg -256 0 0 254 256 0 0 -254 1164 4612 5 MP stroke c8 0 128 256 0 0 -128 1484 4612 4 MP PP 0 sg -256 0 0 128 256 0 0 -128 1484 4612 5 MP stroke c8 0 94 257 0 0 -94 1804 4612 4 MP PP 0 sg -257 0 0 94 257 0 0 -94 1804 4612 5 MP stroke c8 0 77 256 0 0 -77 2125 4612 4 MP PP 0 sg -256 0 0 77 256 0 0 -77 2125 4612 5 MP stroke c8 0 62 256 0 0 -62 2445 4612 4 MP PP 0 sg -256 0 0 62 256 0 0 -62 2445 4612 5 MP stroke c8 0 58 256 0 0 -58 2765 4612 4 MP PP 0 sg -256 0 0 58 256 0 0 -58 2765 4612 5 MP stroke c8 0 70 256 0 0 -70 3085 4612 4 MP PP 0 sg -256 0 0 70 256 0 0 -70 3085 4612 5 MP stroke c8 0 56 256 0 0 -56 3405 4612 4 MP PP 0 sg -256 0 0 56 256 0 0 -56 3405 4612 5 MP stroke c8 0 52 256 0 0 -52 3725 4612 4 MP PP 0 sg -256 0 0 52 256 0 0 -52 3725 4612 5 MP stroke c8 0 52 256 0 0 -52 4045 4612 4 MP PP 0 sg -256 0 0 52 256 0 0 -52 4045 4612 5 MP stroke c8 0 54 256 0 0 -54 4365 4612 4 MP PP 0 sg -256 0 0 54 256 0 0 -54 4365 4612 5 MP stroke c8 0 62 257 0 0 -62 4685 4612 4 MP PP 0 sg -257 0 0 62 257 0 0 -62 4685 4612 5 MP stroke c8 0 66 256 0 0 -66 5006 4612 4 MP PP 0 sg -256 0 0 66 256 0 0 -66 5006 4612 5 MP stroke c8 0 96 256 0 0 -96 5326 4612 4 MP PP 0 sg -256 0 0 96 256 0 0 -96 5326 4612 5 MP stroke c8 0 127 256 0 0 -127 5646 4612 4 MP PP 0 sg -256 0 0 127 256 0 0 -127 5646 4612 5 MP stroke c8 0 937 256 0 0 -937 5966 4612 4 MP PP 0 sg -256 0 0 937 256 0 0 -937 5966 4612 5 MP stroke gr /Helvetica /ISOLatin1Encoding 288 FMSR 2808 5115 mt (Interval size) s 508 3180 mt -90 rotate (Frequency) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 1324 1020 a Fm(\(c\))1395 612 y 8051672 6441336 2368143 11840716 35982622 39008583 startTexFig 1395 612 a %%BeginDocument: figures/ul-16-all.eps % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def MathWorks begin 0 cap end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0204 7344 csm 235 217 6128 4964 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef 1 j 1 sg 0 0 6913 5185 PR 6 w 0 4224 5356 0 0 -4224 898 4612 4 MP PP -5356 0 0 4224 5356 0 0 -4224 898 4612 5 MP stroke 4 w DO SO 6 w 0 sg 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L 898 4612 mt 6254 4612 L 898 4612 mt 898 388 L 898 4612 mt 898 4558 L 898 388 mt 898 442 L /Helvetica /ISOLatin1Encoding 216 FMSR 838 4848 mt (0) s 1969 4612 mt 1969 4558 L 1969 388 mt 1969 442 L 1819 4848 mt (0.2) s 3040 4612 mt 3040 4558 L 3040 388 mt 3040 442 L 2890 4848 mt (0.4) s 4112 4612 mt 4112 4558 L 4112 388 mt 4112 442 L 3962 4848 mt (0.6) s 5183 4612 mt 5183 4558 L 5183 388 mt 5183 442 L 5033 4848 mt (0.8) s 6254 4612 mt 6254 4558 L 6254 388 mt 6254 442 L 6194 4848 mt (1) s 898 4612 mt 952 4612 L 6254 4612 mt 6200 4612 L 743 4692 mt (0) s 898 3767 mt 952 3767 L 6254 3767 mt 6200 3767 L 563 3847 mt (0.2) s 898 2922 mt 952 2922 L 6254 2922 mt 6200 2922 L 563 3002 mt (0.4) s 898 2078 mt 952 2078 L 6254 2078 mt 6200 2078 L 563 2158 mt (0.6) s 898 1233 mt 952 1233 L 6254 1233 mt 6200 1233 L 563 1313 mt (0.8) s 898 388 mt 952 388 L 6254 388 mt 6200 388 L 743 468 mt (1) s 898 4612 mt 6254 4612 L 898 388 mt 6254 388 L 898 4612 mt 898 388 L 6254 4612 mt 6254 388 L gs 898 388 5357 4225 MR c np /c8 { 0.000000 0.000000 0.562500 sr} bdef c8 0 0 255 0 0 0 -115 4612 4 MP PP 0 sg -255 0 0 0 255 0 0 0 -115 4612 5 MP stroke c8 0 0 256 0 0 0 204 4612 4 MP PP 0 sg -256 0 0 0 256 0 0 0 204 4612 5 MP stroke c8 0 1 256 0 0 -1 524 4612 4 MP PP 0 sg -256 0 0 1 256 0 0 -1 524 4612 5 MP stroke c8 0 1261 256 0 0 -1261 844 4612 4 MP PP 0 sg -256 0 0 1261 256 0 0 -1261 844 4612 5 MP stroke c8 0 214 256 0 0 -214 1164 4612 4 MP PP 0 sg -256 0 0 214 256 0 0 -214 1164 4612 5 MP stroke c8 0 122 256 0 0 -122 1484 4612 4 MP PP 0 sg -256 0 0 122 256 0 0 -122 1484 4612 5 MP stroke c8 0 93 257 0 0 -93 1804 4612 4 MP PP 0 sg -257 0 0 93 257 0 0 -93 1804 4612 5 MP stroke c8 0 76 256 0 0 -76 2125 4612 4 MP PP 0 sg -256 0 0 76 256 0 0 -76 2125 4612 5 MP stroke c8 0 60 256 0 0 -60 2445 4612 4 MP PP 0 sg -256 0 0 60 256 0 0 -60 2445 4612 5 MP stroke c8 0 61 256 0 0 -61 2765 4612 4 MP PP 0 sg -256 0 0 61 256 0 0 -61 2765 4612 5 MP stroke c8 0 61 256 0 0 -61 3085 4612 4 MP PP 0 sg -256 0 0 61 256 0 0 -61 3085 4612 5 MP stroke c8 0 53 256 0 0 -53 3405 4612 4 MP PP 0 sg -256 0 0 53 256 0 0 -53 3405 4612 5 MP stroke c8 0 56 256 0 0 -56 3725 4612 4 MP PP 0 sg -256 0 0 56 256 0 0 -56 3725 4612 5 MP stroke c8 0 58 256 0 0 -58 4045 4612 4 MP PP 0 sg -256 0 0 58 256 0 0 -58 4045 4612 5 MP stroke c8 0 59 256 0 0 -59 4365 4612 4 MP PP 0 sg -256 0 0 59 256 0 0 -59 4365 4612 5 MP stroke c8 0 69 257 0 0 -69 4685 4612 4 MP PP 0 sg -257 0 0 69 257 0 0 -69 4685 4612 5 MP stroke c8 0 71 256 0 0 -71 5006 4612 4 MP PP 0 sg -256 0 0 71 256 0 0 -71 5006 4612 5 MP stroke c8 0 112 256 0 0 -112 5326 4612 4 MP PP 0 sg -256 0 0 112 256 0 0 -112 5326 4612 5 MP stroke c8 0 155 256 0 0 -155 5646 4612 4 MP PP 0 sg -256 0 0 155 256 0 0 -155 5646 4612 5 MP stroke c8 0 1640 256 0 0 -1640 5966 4612 4 MP PP 0 sg -256 0 0 1640 256 0 0 -1640 5966 4612 5 MP stroke gr /Helvetica /ISOLatin1Encoding 288 FMSR 2808 5115 mt (Interval size) s 508 3180 mt -90 rotate (Frequency) s 90 rotate end eplot epage end showpage %%EndDocument endTexFig 75 1126 a Fm(Figure)f(12:)22 b(Histograms)13 b(of)h(the)h(size)g(of)e (the)i(in)o(terv)m(al)g(b)q(ounds)g(on)f(all)h(of)f(the)g(diseases)h (in)g(the)f(QMR-)299 1183 y(DT)f(net)o(w)o(ork)g(for)g(\(a\))g(the)g (four)h(tractable)f(CPC)g(cases,)h(\(b\))f(the)h(24)f(selected)i(CPC)e (cases)299 1239 y(from)i(the)g(previous)h(section,)f(and)h(\(c\))e(all) j(of)d(the)i(CPC)e(cases.)75 1420 y(v)m(ariational)20 b(metho)q(d)f(w)o(as)f(run)h(with)g(12)g(p)q(ositiv)o(e)h(\014ndings)g (treated)e(exactly)l(.)32 b(F)l(or)18 b(the)h(remaining)75 1477 y(CPC)d(cases)h(the)g(v)m(ariational)h(metho)q(d)f(w)o(as)g(run)g (with)g(16)f(p)q(ositiv)o(e)i(\014ndings)h(treated)d(exactly)l(.)26 b(The)75 1533 y(running)16 b(time)g(of)f(the)g(algorithm)g(w)o(as)f (less)i(than)f(10)g(seconds)h(of)e(computer)i(time)f(p)q(er)h(CPC)e (case.)146 1601 y(F)l(or)g(the)h(tractable)g(CPC)f(cases,)h(the)g(in)o (terv)m(al)h(b)q(ounds)g(are)f(tigh)o(t)g(for)f(nearly)i(all)g(of)e (the)h(diseases)75 1658 y(in)i(the)e(net)o(w)o(ork.)21 b(Ho)o(w)o(ev)o(er,)15 b(\(1\))f(few)i(of)f(the)h(p)q(ositiv)o(e)h (\014ndings)g(are)f(treated)f(v)m(ariationally)i(in)g(these)75 1714 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{newpath} bdef /nx {/x E def} bdef /r {rmoveto} bdef /rl {rlineto} bdef /rgb {setrgbcolor} bdef /s {show} bdef /sd {setdash} bdef /sp {x 0 rmoveto} bdef /ss {currentpoint pop E m} bdef /st {stroke} bdef /BPSIDE 32 def %% pixels per pattern side /PATFREQ 3.0 def %% pattern pixels per mm /dp_mat [PATFREQ 0 0 PATFREQ 0 0] def /dp_pw BPSIDE def %% pattern pixel width /dp_ph BPSIDE def %% pattern pixel height /dp_w dp_pw PATFREQ div def %% pattern mm width /dp_h dp_ph PATFREQ div def %% pattern mm height /savemat matrix def /topmat matrix def /patmat matrix def /ncpoint errordict /nocurrentpoint get def errordict begin /nocurrentpoint { dup /pathbbox load eq {pop 0 0 1 1} {ncpoint} ifelse } bdef end /ar { %% sa ea sx sy rot tx ty matrix currentmatrix 8 1 roll TR RO SC n 0 0 1 5 3 roll arc setmatrix } bdef /arn { %% sa ea sx sy rot tx ty TR RO SC matrix currentmatrix 8 1 roll n 0 0 1 5 3 roll arcn setmatrix } bdef /el { %% sx sy rot tx ty matrix currentmatrix 6 1 roll TR RO SC n 0 0 1 0 360 arc setmatrix cl } bdef /image_raster { %% sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def /imagebuf sw sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} image } bdef /imagemask_raster { TR SC /sh E def /sw E def /imagebuf sw 7 add 8 idiv string def sw sh false [sw 0 0 sh 0 0] {currentfile imagebuf readhexstring pop} imagemask } bdef /dither_color_raster { % bool sw sh sd dw dh xs ys TR SC /sd E def /sh E def /sw E def sd 8 eq and { /imagebuf 3 string def /grayval 1 string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop pop imagebuf 0 get 0.299 mul imagebuf 1 get 0.587 mul add imagebuf 2 get 0.114 mul add cvi grayval exch 0 exch put grayval } image } { /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sh { currentfile imagebuf readhexstring pop pop } repeat } ifelse } bdef /image_color_raster { % bool sw sh sd dw dh xs ys /colorimage where not { dither_color_raster } { pop TR SC /sd E def /sh E def /sw E def pop /imagebuf sw 3 mul sd mul 7 add 8 idiv string def sw sh sd [sw 0 0 sh 0 0] { currentfile imagebuf readhexstring pop} false 3 colorimage } ifelse } bdef /patpath { /inv E def topmat setmatrix pathbbox %% get lo - hi indecies /hy E dp_h div floor cvi def /hx E dp_w div floor cvi def /ly E dp_h div floor cvi def /lx E dp_w div floor cvi def lx 1 hx { dp_w mul ly 1 hy { dp_h mul E dup 3 1 roll E patmat currentmatrix pop TR dp_pw dp_ph inv dp_mat dp_proc imagemask patmat setmatrix } for pop } for } bdef % setpattern brush of patterns instead of gray /setpattern { /blue E def /green E def /red E def /freq E def /bwidth E def /bpside E def /bstring E def /onbits 0 def /offbits 0 def freq 0 {/y E def /x E def /xindex x 1 add 2 div bpside mul cvi def /yindex y 1 add 2 div bpside mul cvi def bstring yindex bwidth mul xindex 8 idiv add get not 1 7 xindex 8 mod sub bitshift and 0 ne {/onbits onbits 1 add def 1} {/offbits offbits 1 add def 0} ifelse } setscreen {} settransfer systemdict /setcmykcolor known { /fact 1 onbits offbits onbits add div sub def 1 red sub fact mul 1 green sub fact mul 1 blue sub fact mul 0 setcmykcolor } { offbits offbits onbits add div setgray} ifelse } bdef /dmatrix matrix def /dpi 72 0 dmatrix defaultmatrix dtransform dup mul E dup mul add sqrt def /B {gs bp st gr} bdef %% brush: gr lw lj /Bbw {gs bpbw st gr} bdef %% brush: gr lw lj /F {gs rgb eofill gr} bdef %% fill: gr /Fbw {gs setgray eofill gr} bdef %% fill: gr /PB {gs lj lw setpattern st gr} bdef /PF {gs eoclip patpath gr} bdef /BB {gs rgb lj lw strokepath clip patpath gr} bdef /xdef {exch def} bdef /clip_region { /ht xdef /wd xdef /bm xdef /lm xdef newpath lm bm moveto 0 ht rlineto wd 0 rlineto 0 ht neg rlineto closepath clip } bdef /reencode_small_dict 12 dict def /ReencodeSmall { reencode_small_dict begin /new_codes_and_names exch def /new_font_name exch def /base_font_name exch def /base_font_dict base_font_name findfont def /newfont base_font_dict maxlength dict def base_font_dict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName new_font_name put new_codes_and_names aload pop new_codes_and_names length 2 idiv { newfont /Encoding get 3 1 roll put } repeat new_font_name newfont definefont pop end %reencode_small_dict } def /extended_Zapf [ 8#223 /a89 8#224 /a90 8#225 /a93 8#226 /a94 8#227 /a91 8#230 /a92 8#231 /a205 8#232 /a85 8#233 /a206 8#234 /a86 8#235 /a87 8#236 /a88 8#237 /a95 8#240 /a96 ] def /extended_Standard [ 29 /thorn 30 /yacute 31 /divide 128 /Acircumflex 129 /Adieresis 130 /Agrave 131 /Aring 132 /Atilde 133 /Ccedilla 134 /Eacute 135 /Ecircumflex 136 /Edieresis 137 /Egrave 138 /Iacute 139 /Icircumflex 140 /Idieresis 141 /Igrave 142 /Ntilde 143 /Oacute 144 /Ocircumflex 145 /Odieresis 146 /Ograve 147 /Otilde 148 /Scaron 149 /Uacute 150 /Ucircumflex 151 /Udieresis 152 /Ugrave 153 /Ydieresis 154 /Zcaron 155 /aacute 156 /acircumflex 157 /adieresis 158 /agrave 159 /aring 160 /atilde 161 /exclamdown 162 /cent 163 /sterling 164 /fraction 165 /yen 166 /florin 167 /section 168 /currency 169 /quotesingle 170 /quotedblleft 171 /guillemotleft 172 /guilsinglleft 173 /guilsinglright 174 /fi 175 /fl 176 /plusminus 177 /endash 178 /dagger 179 /daggerdbl 180 /periodcentered 181 /twosuperior 182 /paragraph 183 /bullet 184 /quotesinglbase 185 /quotedblbase 186 /quotedblright 187 /guillemotright 188 /ellipsis 189 /perthousand 190 /threesuperior 191 /questiondown 192 /mu 193 /grave 194 /acute 195 /circumflex 196 /tilde 197 /macron 198 /breve 199 /dotaccent 200 /dieresis 201 /onesuperior 202 /ring 203 /cedilla 204 /onequarter 205 /hungarumlaut 206 /ogonek 207 /caron 208 /emdash 209 /ccedilla 210 /copyright 211 /eacute 212 /ecircumflex 213 /edieresis 214 /egrave 215 /iacute 216 /icircumflex 217 /idieresis 218 /igrave 219 /logicalnot 220 /minus 221 /ntilde 222 /oacute 223 /ocircumflex 224 /odieresis 225 /AE 226 /onehalf 227 /ordfeminine 228 /ograve 229 /otilde 230 /registered 231 /scaron 232 /Lslash 233 /Oslash 234 /OE 235 /ordmasculine 236 /trademark 237 /uacute 238 /ucircumflex 239 /udieresis 240 /ugrave 241 /ae 242 /ydieresis 243 /zcaron 244 /Aacute 245 /dotlessi 246 /threequarters 247 /Eth 248 /lslash 249 /oslash 250 /oe 251 /germandbls 252 /multiply 253 /Yacute 254 /Thorn 255 /eth ] def /extended_Symbol [ ] def /extend_font { % stack: fontname newfontname exch dup (ZapfDingbats) eq { cvn exch cvn extended_Zapf ReencodeSmall } { dup (Symbol) eq { cvn exch cvn extended_Symbol ReencodeSmall } { cvn exch cvn extended_Standard ReencodeSmall } ifelse } ifelse } bind def /extend_font_name { % stack: font_name_string dup length 1 add string /extended_font_name exch def extended_font_name 0 (_) putinterval extended_font_name 1 3 -1 roll putinterval extended_font_name } bind def /gf { /f exch def f cvn where { f exch begin cvn load exec setfont end } { f 0 f length 8 sub getinterval dup /localfont exch 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Fm(Sev)o(eral)d(observ)m(ations)f(are)g(in)h(order.)19 b(Recall)14 b(that)e Fi(f)1001 108 y Fl(\003)1020 124 y Fm(\()p Fi(\030)1058 131 y Fj(i)1072 124 y Fm(\))g(is)h(the)f (conjugate)g(of)g(the)g(conca)o(v)o(e)g(function)75 181 y Fi(f)27 b Fm(\(the)22 b(exp)q(onen)o(t\),)i(and)f(is)f(therefore)g (also)h(conca)o(v)o(e;)i(for)c(this)i(reason)f Fg(\000)p Fi(f)1481 164 y Fl(\003)1501 181 y Fm(\()p Fi(\030)1539 188 y Fj(i)1553 181 y Fm(\))g(is)g(con)o(v)o(ex.)41 b(In)75 237 y(App)q(endix)17 b(C)e(w)o(e)g(pro)o(v)o(e)g(that)f(the)i (remaining)g(term:)710 350 y(log)9 b Fi(E)820 290 y Ff(\032)851 350 y Fi(e)880 296 y Ff(P)924 340 y Fe(j;i)p Fc(\024)p Fe(m)1017 325 y Fj(\030)1033 330 y Fe(i)1045 325 y Fj(\022)1061 330 y Fe(ij)1089 325 y Fj(d)1107 330 y Fe(j)1126 290 y Ff(\033)1794 350 y Fm(\(45\))75 462 y(is)21 b(also)g(a)g(con)o(v)o (ex)g(function)h(of)e(the)h(v)m(ariational)h(parameters.)36 b(No)o(w,)22 b(since)g(an)o(y)f(sum)g(of)f(con)o(v)o(ex)75 519 y(functions)g(is)f(con)o(v)o(ex,)g(w)o(e)g(conclude)i(that)d(log)8 b Fi(P)e Fm(\()p Fi(f)1000 502 y Ft(+)1030 519 y Fg(j)p Fi(\030)r Fm(\))18 b(is)h(a)g(con)o(v)o(ex)g(function)h(of)e(the)h(v)m (ariational)75 575 y(parameters.)k(This)17 b(means)f(that)g(there)h (are)f(no)g(lo)q(cal)i(minima)f(in)h(our)e(optimization)h(problem.)25 b(W)l(e)75 632 y(ma)o(y)18 b(safely)i(emplo)o(y)f(the)g(standard)g (Newton-Raphson)g(pro)q(cedure)h(to)e(solv)o(e)i Fg(r)8 b Fm(log)f Fi(P)f Fm(\()p Fi(f)1684 615 y Ft(+)1714 632 y Fg(j)p Fi(\030)r Fm(\))18 b(=)i(0.)75 688 y(Alternativ)o(ely)13 b(w)o(e)e(can)h(utilize)i(\014xed-p)q(oin)o(t)f(iterations.)19 b(In)12 b(particular,)h(w)o(e)e(calculate)i(the)f(deriv)m(ativ)o(es)75 745 y(of)f(the)h(v)m(ariational)h(form)e(and)g(iterativ)o(ely)i(solv)o (e)f(for)f(the)h(individual)i(v)m(ariational)f(parameters)e Fi(\030)1755 752 y Fj(k)1788 745 y Fm(suc)o(h)75 801 y(that)j(the)i(deriv)m(ativ)o(es)g(are)f(zero.)20 b(The)15 b(deriv)m(ativ)o(es)i(are)e(giv)o(en)g(as)g(follo)o(ws:)464 908 y Fi(@)p 443 928 68 2 v 443 970 a(@)s(\030)490 977 y Fj(k)524 938 y Fm(log)8 b Fi(P)e Fm(\()p Fi(f)670 920 y Ft(+)700 938 y Fg(j)p Fi(\030)r Fm(\))41 b(=)h Fi(\022)892 945 y Fj(k)q Ft(0)941 938 y Fm(+)11 b(log)1097 908 y Fi(\030)1117 915 y Fj(k)p 1058 928 120 2 v 1058 970 a Fm(1)f(+)g Fi(\030)1156 977 y Fj(k)1192 938 y Fm(+)h Fi(E)1282 852 y Ff(8)1282 890 y(<)1282 964 y(:)1318 898 y(X)1340 989 y Fj(j)1386 938 y Fi(\022)1407 945 y Fj(k)q(j)1445 938 y Fi(d)1469 945 y Fj(j)1487 852 y Ff(9)1487 890 y(=)1487 964 y(;)1794 938 y Fm(\(46\))444 1074 y Fi(@)471 1057 y Ft(2)p 424 1094 88 2 v 424 1136 a Fi(@)451 1123 y Ft(2)470 1136 y Fi(\030)490 1143 y Fj(k)524 1105 y Fm(log)d Fi(P)e Fm(\()p Fi(f)670 1086 y Ft(+)700 1105 y Fg(j)p Fi(\030)r Fm(\))41 b(=)885 1074 y(1)p 876 1094 42 2 v 876 1136 a Fi(\030)896 1143 y Fj(k)932 1105 y Fg(\000)1031 1074 y Fm(1)p 982 1094 120 2 v 982 1136 a(1)10 b(+)h Fi(\030)1081 1143 y Fj(k)1117 1105 y Fm(+)f(V)q Fi(ar)1250 1018 y Ff(8)1250 1056 y(<)1250 1131 y(:)1287 1064 y(X)1309 1155 y Fj(j)1354 1105 y Fi(\022)1375 1112 y Fj(k)q(j)1413 1105 y Fi(d)1437 1112 y Fj(j)1455 1018 y Ff(9)1455 1056 y(=)1455 1131 y(;)1500 1105 y Fi(;)281 b Fm(\(47\))75 1242 y(where)20 b(the)f(exp)q(ectation)i(and)f(the)f(v)m(ariance)i(are) e(with)h(resp)q(ect)g(to)f(the)g(p)q(osterior)h(appro)o(ximation)75 1298 y Fi(P)6 b Fm(\()p Fi(d)p Fg(j)p Fi(f)192 1282 y Ft(+)221 1298 y Fi(;)i(\030)r Fm(\),)16 b(and)h(b)q(oth)h(deriv)m(ativ) o(es)g(can)f(b)q(e)h(computed)g(in)f(time)h(linear)g(in)g(the)f(n)o(um) o(b)q(er)h(of)e(asso)q(ci-)75 1355 y(ated)i(diseases)g(for)f(the)h (\014nding.)29 b(The)18 b(b)q(enign)i(scaling)f(of)e(the)h(v)m(ariance) h(calculations)g(comes)f(from)75 1411 y(exploiting)12 b(the)f(sp)q(ecial)i(prop)q(erties)e(of)g(the)f(noisy-OR)j(dep)q (endence)g(and)e(the)g(marginal)g(indep)q(endence)75 1468 y(of)k(the)g(diseases.)146 1524 y(Calculating)g(the)g(exp)q 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b(\(T)l(o)11 b(b)q(e)h(precise,)75 1919 y(in)j(the)e(case)h(of)g(8,)f(12)g(and)h(16) f(total)h(\014ndings)h(treated)e(exactly)l(,)h(w)o(e)g(optimized)h(the) f(parameters)f(after)75 1976 y(4,)i(8,)f(and)h(8)g(\014ndings,)h(resp)q (ectiv)o(ely)l(,)h(w)o(ere)e(in)o(tro)q(duced\).)75 2092 y Fr(Lo)o(w)o(er)h(Bound)i(T)l(ransformations)75 2173 y Fm(Mimic)o(king)24 b(the)f(case)f(of)g(upp)q(er)i(b)q(ounds,)h(w)o(e) d(replace)i(individual)h(conditional)g(probabilities)f(of)75 2229 y(the)14 b(\014ndings)h(with)f(lo)o(w)o(er-b)q(ounding)h (transformations,)d(resulting)j(in)g(a)e(lo)o(w)o(er-b)q(ounding)i (expression)75 2286 y Fi(P)6 b Fm(\()p Fi(f)155 2269 y Ft(+)185 2286 y Fg(j)p Fi(d;)i(q)r Fm(\).)24 b(T)l(aking)17 b(the)h(pro)q(duct)f(with)h Fi(P)6 b Fm(\()p Fi(d)p Fm(\))17 b(and)g(marginalizing)i(o)o(v)o(er)e Fi(d)f Fm(yields)j(a)e(lo)o(w)o (er)g(b)q(ound)75 2342 y(on)e(the)g(lik)o(eliho)q(o)q(d:)538 2437 y Fi(P)6 b Fm(\()p Fi(f)618 2418 y Ft(+)648 2437 y Fm(\))12 b Fg(\025)726 2397 y 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Fm(\()p Fi(f)683 221 y Ft(+)713 237 y Fg(j)p Fi(q)r Fm(\))k(\(or)h(its)g(logarithm\))f(can)i(b)q(e)f(view)o(ed)h(as) f(a)f(standard)h(maxim)o(um)75 294 y(lik)o(eliho)q(o)q(d)20 b(estimation)e(problem)f(for)g(a)g(laten)o(t)g(v)m(ariable)h(mo)q(del.) 27 b(It)17 b(can)h(b)q(e)g(solv)o(ed)f(using)h(the)f(EM)75 350 y(algorithm)12 b(\(Dempster,)f(Laird,)i(&)f(Rubin,)i(1977\).)j(The) 12 b(algorithm)f(yields)j(a)d(sequence)i(of)e(v)m(ariational)75 407 y(parameters)i(that)f(monotonically)j(increase)f(the)f(ob)s(jectiv) o(e)h(function)g(log)8 b Fi(P)e Fm(\()p Fi(f)1458 390 y Ft(+)1488 407 y Fg(j)p Fi(q)r Fm(\).)18 b(Within)d(the)e(EM)75 463 y(framew)o(ork,)g(w)o(e)h(obtain)g(an)g(up)q(date)h(of)f(the)g(v)m (ariational)h(parameters)f(b)o(y)g(maximizing)h(the)g(exp)q(ected)75 519 y(complete)h(log-lik)o(eliho)q(o)q(d:)305 624 y Fi(E)349 590 y Ff(\010)380 624 y Fm(log)9 b Fi(P)d Fm(\()p Fi(f)527 606 y Ft(+)557 624 y Fg(j)p Fi(d;)i(q)r Fm(\))p Fi(P)e Fm(\()p Fi(d)p Fm(\))758 590 y Ff(\011)792 624 y 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y(parameters)g(asso)q(ciated)h(with)g(the)f(conditional)j (probabilities)g Fi(P)6 b Fm(\()p Fi(f)1263 917 y Ft(+)1258 949 y Fj(i)1292 936 y Fg(j)p Fi(d;)i(q)1370 945 y Fl(\001j)p Fj(i)1403 936 y Fm(\))j(are)h(indep)q(enden)o(t)i(of)d(one)75 992 y(another,)i(w)o(e)g(can)g(maximize)h(eac)o(h)f(term)g(in)h(the)f (ab)q(o)o(v)o(e)g(sum)g(separately)l(.)20 b(Recalling)15 b(the)f(form)e(of)h(the)75 1049 y(v)m(ariational)j(transformation)e (\(see)h(Eq.)g(\(24\)\),)e(w)o(e)i(ha)o(v)o(e:)290 1181 y Fi(E)334 1134 y Ff(n)369 1181 y Fm(log)9 b Fi(P)d Fm(\()p Fi(f)516 1162 y Ft(+)511 1194 y Fj(i)545 1181 y Fg(j)p Fi(d;)i(q)623 1190 y Fl(\001j)p Fj(i)656 1181 y Fm(\))682 1134 y Ff(o)750 1181 y Fm(=)827 1141 y Ff(X)849 1232 y Fj(j)895 1181 y Fi(q)915 1190 y Fj(j)r Fl(j)p Fj(i)963 1181 y Fi(E)s Fg(f)p Fi(d)1047 1188 y Fj(j)1063 1181 y Fg(g)1101 1109 y Ff(")1133 1181 y Fi(f)1168 1109 y Ff( )1208 1181 y Fi(\022)1229 1188 y Fj(io)1271 1181 y Fm(+)1326 1150 y Fi(\022)1347 1157 y Fj(ij)p 1321 1171 61 2 v 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Fi(Z)725 1132 y Ft(2)722 1162 y Fj(k)755 1151 y Fg(\000)10 b Fm(\()818 1111 y Ff(X)838 1203 y Fj(k)885 1151 y Fi(q)905 1158 y Fj(k)927 1151 y Fi(Z)958 1158 y Fj(k)979 1151 y Fm(\)\()1015 1111 y Ff(X)1039 1203 y Fj(l)1082 1151 y Fi(q)1102 1158 y Fj(l)1116 1151 y Fi(Z)1147 1158 y Fj(l)1160 1151 y Fm(\))i(=)h(V)p Fi(ar)q Fg(f)p Fi(Z)s Fg(g)f(\025)h Fm(0)313 b(\(56\))75 1291 y(where)18 b(V)p Fi(ar)q Fg(f)p Fi(Z)s Fg(g)g Fm(is)h(the)f(v)m (ariance)h(of)e(a)h(discrete)h(random)f(v)m(ariable)h Fi(Z)i Fm(whic)o(h)e(tak)o(es)f(the)g(v)m(alues)h Fi(Z)1861 1298 y Fj(i)75 1347 y Fm(with)d(probabilit)o(y)g Fi(q)431 1354 y Fj(i)445 1347 y Fm(.)75 1477 y Fo(References)75 1564 y Fm(D'Am)o(brosio,)j(B.)g(\(1993\).)30 b(Incremen)o(tal)20 b(probabilistic)i(inference.)34 b(In)19 b Fh(Pr)n(o)n(c)n(e)n(e)n (dings)f(of)i(the)g(Ninth)193 1620 y(Confer)n(enc)n(e)15 b(on)i(Unc)n(ertainty)f(in)g(A)o(rti\014cial)h(Intel)r(ligenc)n(e)p Fm(.)i(San)d(Mateo,)f(CA:)h(Morgan)f(Kauf-)193 1677 y(mann.)75 1777 y(D'Am)o(brosio,)h(B.)h(\(1994\).)23 b(Sym)o(b)q(olic)18 b(probabilistic)h(inference)g(in)e(large)g(BN20)g(net)o(w)o(orks.)23 b(In)18 b Fh(Pr)n(o-)193 1833 y(c)n(e)n(e)n(dings)11 b(of)i(the)h(T)m(enth)e(Confer)n(enc)n(e)f(on)i(Unc)n(ertainty)f(in)g (A)o(rti\014cial)g(Intel)r(ligenc)n(e)p Fm(.)k(San)c(Mateo,)193 1890 y(CA:)j(Morgan)f(Kaufmann.)75 1990 y(Co)q(op)q(er,)24 b(G.)d(\(1985\).)39 b Fh(NESTOR:)22 b(A)g(c)n(omputer-b)n(ase)n(d)h(me) n(dic)n(al)f(diagnostic)h(aid)g(that)g(inte)n(gr)n(ates)193 2046 y(c)n(ausal)15 b(and)g(pr)n(ob)n(abilistic)g(know)r(le)n(dge)p Fm(.)k(Ph.D.)13 b(Dissertation,)h(Medical)h(Informatics)g(Sciences,)193 2103 y(Stanford)10 b(Univ)o(ersit)o(y)l(,)h(Stanford,)g(CA.)e(\(Av)m (ailable)j(from)e(UMI)g(at)g(h)o (ttp://wwwlib.umi.com/dissertations/main\).)75 2203 y(Co)q(op)q(er,)j (G.)g(\(1990\).)18 b(The)13 b(computational)h(complexit)o(y)g(of)f (probabilistic)j(inference)f(using)f(Ba)o(y)o(esian)193 2259 y(b)q(elief)j(net)o(w)o(orks.)i Fh(A)o(rti\014cial)c(Intel)r (ligenc)n(e)p Fm(,)e Fh(42)p Fm(,)i(393{405.)75 2359 y(Dagum,)23 b(P)l(.,)h(&)f(Horvitz,)i(E.)d(\(1992\).)40 b(Reform)o(ulating)24 b(inference)g(problems)f(through)g(selectiv)o(e) 193 2416 y(conditioning.)44 b(In)23 b Fh(Pr)n(o)n(c)n(e)n(e)n(dings)e (of)i(the)g(Eighth)h(A)o(nnual)e(Confer)n(enc)n(e)f(on)h(Unc)n (ertainty)h(in)193 2472 y(A)o(rti\014cial)15 b(Intel)r(ligenc)n(e)p Fm(.)75 2572 y(Dagum,)d(P)l(.,)g(&)g(Horvitz,)g(E.)g(\(1993\).)17 b(A)12 b(Ba)o(y)o(esian)g(analysis)h(of)e(sim)o(ulation)i(algorithms)f (for)f(inference)193 2629 y(in)16 b(Belief)h(net)o(w)o(orks.)i Fh(Networks)p Fm(,)14 b Fh(23)p Fm(,)i(499{516.)954 2753 y Fn(30)p eop %%Page: 31 31 31 30 bop 431 -100 a Fq(V)-5 b(aria)m(tional)17 b(Pr)o(obabilistic)e (Inference)h(and)h(QMR-DT)75 124 y Fm(Dagum,)j(P)l(.,)h(&)g(Lub)o(y)l (,)h(M.)e(\(1993\).)33 b(Appro)o(ximate)20 b(probabilistic)j(reasoning) d(in)i(Ba)o(y)o(esian)e(b)q(elief)193 181 y(net)o(w)o(orks)14 b(is)i(NP-hard.)k Fh(A)o(rti\014cial)15 b(Intel)r(ligenc)n(e)p Fm(,)d Fh(60)p Fm(,)k(141{153.)75 286 y(Dec)o(h)o(ter,)e(R.)h (\(1997\).)j(Mini-buc)o(k)o(ets:)j(A)15 b(general)g(sc)o(heme)g(of)g (generating)g(appro)o(ximations)g(in)g(auto-)193 343 y(mated)i(reasoning.)27 b(In)17 b Fh(Pr)n(o)n(c)n(e)n(e)n(dings)f(of)j (the)f(Fifte)n(enth)f(International)g(Joint)h(Confer)n(enc)n(e)e(on)193 399 y(A)o(rti\014cial)f(Intel)r(ligenc)n(e)p Fm(.)75 505 y(Dec)o(h)o(ter,)h(R.)h(\(1998\).)24 b(Buc)o(k)o(et)17 b(elimination:)25 b(A)17 b(unifying)i(framew)o(ork)c(for)i (probabilistic)i(inference.)193 562 y(In)d(M.)e(I.)i(Jordan)f(\(Ed.\),) f Fh(L)n(e)n(arning)g(in)i(Gr)n(aphic)n(al)g(Mo)n(dels)p Fm(.)j(Cam)o(bridge,)c(MA:)f(MIT)i(Press.)75 667 y(Dempster,)h(A.,)f (Laird,)i(N.,)f(&)g(Rubin,)i(D.)d(\(1977\).)23 b(Maxim)o(um)17 b(lik)o(eliho)q(o)q(d)j(from)c(incomplete)j(data)193 724 y(via)d(the)f(EM)g(algorithm.)20 b Fh(Journal)c(of)g(the)h(R)n (oyal)f(Statistic)n(al)f(So)n(ciety)h(B)p Fm(,)f Fh(39)p Fm(,)g(1{38.)75 830 y(Drap)q(er,)j(D.,)g(&)g(Hanks,)h(S.)e(\(1994\).)27 b(Lo)q(calized)20 b(partial)f(ev)m(aluation)g(of)f(b)q(elief)i(net)o(w) o(orks.)27 b(In)19 b Fh(Pr)n(o-)193 886 y(c)n(e)n(e)n(dings)14 b(of)j(the)f(T)m(enth)f(A)o(nnual)h(Confer)n(enc)n(e)e(on)i(Unc)n (ertainty)f(in)h(A)o(rti\014cial)f(Intel)r(ligenc)n(e)p Fm(.)75 992 y(F)l(ung,)i(R.,)g(&)g(Chang,)g(K.)g(C.)f(\(1990\).)24 b(W)l(eigh)o(ting)17 b(and)g(in)o(tegrating)g(evidence)i(for)e(sto)q(c) o(hastic)f(sim-)193 1048 y(ulation)i(in)g(Ba)o(y)o(esian)f(net)o(w)o (orks.)24 b(In)17 b Fh(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)j(Fifth)g (Confer)n(enc)n(e)e(on)i(Unc)n(ertainty)f(in)193 1105 y(A)o(rti\014cial)e(Intel)r(ligenc)n(e)p Fm(.)j(Amsterdam:)h(Elsevier)d (Science.)75 1211 y(Gelfand,)f(A.,)f(&)h(Smith,)g(A.)f(\(1990\).)k (Sampling-based)e(approac)o(hes)f(to)f(calculating)i(marginal)f(Den-) 193 1267 y(sities.)21 b Fh(Journal)16 b(of)h(the)f(A)o(meric)n(an)g (Statistic)n(al)f(Asso)n(ciation)p Fm(,)e Fh(85)p Fm(,)j(398{409.)75 1373 y(Hec)o(k)o(erman,)e(D.)f(\(1989\).)18 b(A)c(tractable)g (inference)i(algorithm)e(for)f(diagnosing)i(m)o(ultiple)h(diseases.)k (In)193 1429 y Fh(Pr)n(o)n(c)n(e)n(e)n(dings)14 b(of)i(the)h(Fifth)f (Confer)n(enc)n(e)e(on)i(Unc)n(ertainty)g(in)f(A)o(rti\014cial)h(Intel) r(ligenc)n(e)p Fm(.)75 1535 y(Henrion,)h(M.)e(\(1991\).)20 b(Searc)o(h-based)d(metho)q(ds)f(to)g(b)q(ound)g(diagnostic)h (probabilities)h(in)f(v)o(ery)f(large)193 1592 y(b)q(elief)h(nets.)i (In)c Fh(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)j(Seventh)f(Confer)n(enc)n(e)e (on)j(Unc)n(ertainty)e(in)h(A)o(rti\014cial)g(Intel)r(li-)193 1648 y(genc)n(e)p Fm(.)75 1754 y(Horvitz,)e(E.)g(Suermondt,)h(H.,)f(&)g (Co)q(op)q(er,)h(G.)e(\(1989\).)18 b(Bounded)c(conditioning:)21 b(Flexible)15 b(inference)193 1810 y(for)j(decisions)j(under)f(scarce)f (resources.)31 b(In)19 b Fh(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)j(Fifth)g (Confer)n(enc)n(e)d(on)j(Unc)n(er-)193 1867 y(tainty)c(in)g(A)o (rti\014cial)f(Intel)r(ligenc)n(e)p Fm(.)75 1972 y(Jaakk)o(ola,)k(T.)f (\(1997\).)28 b Fh(V)m(ariational)19 b(metho)n(ds)h(for)g(infer)n(enc)n (e)d(and)j(le)n(arning)e(in)h(gr)n(aphic)n(al)g(mo)n(dels)p Fm(.)193 2029 y(PhD)c(thesis,)h(Departmen)o(t)f(of)g(Brain)h(and)f (Cognitiv)o(e)h(Sciences,)h(Massac)o(h)o(usetts)d(Institute)i(of)193 2085 y(T)l(ec)o(hnology)l(.)75 2191 y(Jaakk)o(ola,)i(T.,)f(&)h(Jordan,) g(M.)f(\(1996\).)26 b(Recursiv)o(e)19 b(algorithms)f(for)f(appro)o (ximating)h(probabilities)193 2248 y(in)d(graphical)g(mo)q(dels.)20 b(In)15 b Fh(A)n(dvanc)n(es)f(of)h(Neur)n(al)h(Information)e(Pr)n(o)n (c)n(essing)f(Systems)i(9)p Fm(.)k(Cam-)193 2304 y(bridge,)d(MA:)e(MIT) h(Press.)75 2410 y(Jensen,)22 b(C.)e(S.,)h(Kong,)g(A.,)g(&)f (Kj\032rul\013,)h(U.)f(\(1995\).)33 b(Blo)q(c)o(king-Gibbs)23 b(sampling)e(in)g(v)o(ery)f(large)193 2466 y(probabilistic)d(exp)q(ert) e(systems.)k Fh(International)14 b(Journal)i(of)g(Human-Computer)h (Studies)p Fm(,)d Fh(42)p Fm(,)193 2523 y(647{666.)75 2629 y(Jensen,)i(F.)e(\(1996\).)19 b 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y(Kaufmann.)75 1233 y(P)o(eng,)12 b(Y.,)g(&)g(Reggia,)h(J.)f (\(1987\).)17 b(A)12 b(probabilistic)i(causal)e(mo)q(del)h(for)e (diagnostic)i(problem)g(solving)f({)193 1289 y(P)o(art)f(2:)18 b(Diagnostic)12 b(strategy)l(.)18 b Fh(IEEE)12 b(T)m(r)n(ans.)19 b(on)13 b(Systems,)g(Man,)g(and)h(Cyb)n(ernetics:)j(Sp)n(e)n(cial)193 1346 y(Issue)e(for)i(Diagnosis)p Fm(,)d Fh(17)p Fm(,)h(395{406.)75 1446 y(P)o(o)q(ole,)f(D.)f(\(1997\).)k(Probabilistic)f(partial)e(ev)m (aluation:)20 b(Exploiting)15 b(rule)g(structure)e(in)i(probabilistic) 193 1502 y(inference.)21 b(In)14 b Fh(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)i (the)h(Fifte)n(enth)e(International)g(Joint)h(Confer)n(enc)n(e)f(on)h (A)o(rti\014cial)193 1558 y(Intel)r(ligenc)n(e)p Fm(.)75 1658 y(Ro)q(c)o(k)m(afellar,)i(R.)f(\(1972\).)k Fh(Convex)c(A)o (nalysis)p Fm(.)j(Princeton)e(Univ)o(ersit)o(y)g(Press.)75 1759 y(Shac)o(h)o(ter,)11 b(R.)g(D.,)g(&)h(P)o(eot,)f(M.)f(\(1990\).)17 b(Sim)o(ulation)12 b(approac)o(hes)f(to)f(general)i(probabilistic)h (inference)193 1815 y(on)19 b(b)q(elief)h(net)o(w)o(orks.)29 b(In)19 b Fh(Pr)n(o)n(c)n(e)n(e)n(dings)e(of)j(Fifth)f(Confer)n(enc)n (e)e(on)j(Unc)n(ertainty)e(in)h(A)o(rti\014cial)193 1871 y(Intel)r(ligenc)n(e)p Fm(.)e(Elsevier)g(Science:)22 b(Amsterdam.)75 1971 y(Sheno)o(y)l(,)c(P)l(.)f(P)l(.)g(\(1992\).)24 b(V)l(aluation-based)19 b(systems)e(for)g(Ba)o(y)o(esian)g(decision)i (analysis.)27 b Fh(Op)n(er)n(ations)193 2028 y(R)n(ese)n(ar)n(ch,)15 b(40)p Fm(,)h(463{484.)75 2128 y(Sh)o(w)o(e,)e(M.,)g(&)h(Co)q(op)q(er,) g(G.)f(\(1991\).)j(An)e(empirical)i(analysis)f(of)e(lik)o(eliho)q(o)q (d)j({)e(w)o(eigh)o(ting)g(sim)o(ulation)193 2184 y(on)k(a)g(large,)h (m)o(ultiply)h(connected)g(medical)f(b)q(elief)i(net)o(w)o(ork.)31 b Fh(Computers)20 b(and)g(Biome)n(dic)n(al)193 2241 y(R)n(ese)n(ar)n (ch)p Fm(,)14 b Fh(24)p Fm(,)h(453-475.)75 2341 y(Sh)o(w)o(e,)20 b(M.,)e(Middleton,)j(B.,)e(Hec)o(k)o(erman,)h(D.,)f(Henrion,)h(M.,)f (Horvitz,)h(E.,)f(Lehmann,)h(H.,)f(&)h(G.)193 2397 y(Co)q(op)q(er)h (\(1991\).)35 b(Probabilistic)22 b(diagnosis)g(using)f(a)g(reform)o (ulation)f(of)h(the)g(INTERNIST-)193 2454 y(1/QMR)12 b(kno)o(wledge)h(base)f(I.)g(The)h(probabilistic)h(mo)q(del)f(and)g (inference)g(algorithms.)19 b Fh(Metho)n(ds)193 2510 y(of)e(Information)e(in)h(Me)n(dicine)p Fm(,)e Fh(30)p Fm(,)h(241{255.)954 2753 y Fn(32)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF