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All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 14 /delta put dup 27 /sigma put dup 58 /period put dup 59 /comma put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 84 /T put readonly def /FontBBox{-58 -250 1195 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: TeX-cmex7 %!PS-AdobeFont-1.0: TeX-cmex7 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex7) def /FullName (TeX\040cmex7\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 16 /quotedblleft put dup 17 /quotedblright put readonly def /FontBBox {-14 -2954 1627 771} readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 13 /gamma put dup 105 /i put dup 106 /j put dup 116 /t put readonly def /FontBBox{37 -250 1349 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put dup 49 /one put dup 50 /two put readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F D1F017CE45884D76EF2CB9BC5821FD25365DDEA1F9B0FF4CFF25B8E64D0747A3 7CAD14E0DBA3E3CA95F10F24B7D5D75451845F1FB7221D7794A860756CFBB3E7 704A52A22448C34812C3DBEDD41892577AABA7D555E9298C1A0F7DA638078167 F56E29672683C51CF1C003764A8E7AD9D8ADE77B4983F56FE2D12723AAD8BF36 682CFBB71B1D12210144D39DD841A971F71DB82AC6CD815987CDCF29ABC3CC96 5EEBD5D661F452C6E0C74F9ED8D0C5B3755551A172E0FE31EA02344176E32666 14B6853A1C303A5E818C2E455A6CF8FC9A66DC6E279101D61C523BD9DB8EB82F EAF4D7FDF6372383C0794C4568D079648689A199D4B65BA646CF95B7647E4BEC 83856C27A8EF177B3A686EDA6354FE9573E123C12EC4BA56A7E8BFB8F9B75147 9DD79A743968F36F7D0D479FA610F0816E6267E5CE327686A5485AB72201525C FB3B7CA10E1BF26E44C24E1696CB089CB0055BD692C89B237CF269F77A31DC81 0F4B75C8400ABCFDCEC6443CD0E81871CD71AA3064ABDE882C4C52322C27FA8B 41C689F827FB0F8AAF8022CF3C1F41C0B45601190C1328831857CBF9B1E7D1AA 246117E56D6B7938488055F4E63E2A1C8D57C17D213729C68349FEC2C3466F41 171E00413D39DF1F67BC15912F30775AFDF7FB3312587E20A68CF77AD3906040 842D63C45E19278622DD228C18ABDD024DD9613CDC0B109095DB0ADC3A3C0CB5 AB597D490189EA81239E39202CBC7A829EB9B313A8F962F7879D374ADF529BD0 5533EF977142F647AD2F5975BA7E340419116099B19ACCCC37C551233C89EBC5 0CEFDB2C5FA1AE7F2728AC2CCFF00B5F241264A144705AF954F8C422610B29A4 4BF70F0D12764CFF9A8B641FA4A51B134A83413EED4A3BECC8566CC234A5F07C 40302603F38D74777F0EA1437DDD87B2817B1E34446C77D8C5F9445ABD772166 3806ADB65BE61DD8937EB42E9B748684C87622EE62BD93003AD8AA9D071684DE 7B9F48DFFC26418D8DDCE0738ADADBC2D93CC7E82F8F89964EECDD492B68587F B52414FCC3C1874704C141D67F37AF2E7BB76DAD93E89BDD89FEB7D086903B61 DEBD3540313BD2BD5218388BCFCE17D2B2FF0704C06861A7F540144E02A4AAB4 D5F7F09B0174FFA6A786A0765F2D7CDB351D279A9E13CC8535B62DF672B126B4 5324B18C3E80EAA4452083C44D1747F4D709B48DD1E30AAEBC47BD5ED705D887 D311986F148EE576ED0139B4FDF5AE69F35DC114348F9DA0DE86BE53DFF78BC9 759A84C053F7612D7693390F5F4233084EFB87E50014F85C11F0C2D705EE72E4 CD362720C43226C83C21CAB3B56A483F14725BFD45A536938935744C43393F49 3B3AEDEE368D3F844213C5A4AB7BC82501F8152D3C49048CE32BD5BA27F7A628 093CE17E8AFFF957AC806BA3C6FE79186969F5F242E371FE9C8DFF640FE45FCE F69C98E111EF51C4F34948CADBE8204D2415D5024E97254A4F70B1CB45EE30B2 7E8C233B03497465AD0A1A670039214E201481FD821CE4A663E0EF5E6481F970 13CFF5170E2E983D29F6182FD1E179B60F6AB802560E4140EF9A6B8A341B2295 DCD9B13016E4A62411B2D6223E0447F15C330AF3A32BEC2997D77FA69D2A38AA 87E3FAF36FFC9864973FC7BFEDAC54464F1C96905259E37B912BABBC9CA8A39A 14F2CB78281A06E768B461AE3F965C7E20492A8FB0F434852FF0166B59413703 0900B0EE39BB51C0110E 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put readonly def /FontBBox{21 -944 1448 791}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 2 /Theta put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 58 /colon put dup 61 /equal put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 21 /greaterequal put dup 50 /element put dup 98 /floorleft put dup 99 /floorright put dup 100 /ceilingleft put dup 101 /ceilingright put dup 106 /bar put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 59 /comma put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 84 /T put dup 87 /W put dup 90 /Z put dup 105 /i put dup 106 /j put dup 111 /o put dup 112 /p put dup 113 /q put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 6 /Sigma put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 101 /e put dup 103 /g put dup 108 /l put dup 109 /m put dup 111 /o put dup 112 /p put dup 114 /r put dup 120 /x put readonly def /FontBBox{-39 -250 1036 750}readonly def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 27 /sigma put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 69 /E put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 83 /S put dup 84 /T put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 100 /d put dup 105 /i put dup 106 /j put dup 112 /p put dup 113 /q put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-29 -250 1075 750}readonly def currentdict end currentfile 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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b(produces)f(samples)h(from)f(a)g(sequence)i(of)e (such)g(distrib)-20 b(utions)337 b(for)27024 51304 y(increasing)282 b(v)-25 b(alues)282 b(of)f Fq(\015)57 b Fs(.)407 b(Just)281 b(as)g(in)h(SA,)g(this)f(concentrates)i(the)f(mass)f(on)27024 52461 y(the)253 b(set)f(of)h(global)g(maxima)g(of)g Fq(p)p Fp(\()p Fq(y)36 b Fo(j)p Fq(\022)28 b Fp(\))254 b Fs(as)f Fq(\015)309 b Fs(becomes)254 b(lar)-18 b(ge.)320 b(Another)253 b(ap-)27024 53618 y(proach)221 b(proposed)h(by)f([4])g(is)f(to)h (construct)h(a)f(homogeneous)h(Mark)-10 b(o)-15 b(v)221 b(chain)27024 54774 y(whose)362 b(in)-40 b(v)-25 b(ariant)363 b(distrib)-20 b(ution)362 b(corresponds)f(to)i(such)f(a)g(distrib)-20 b(ution)362 b(for)27024 55931 y(a)308 b(predetermined)h(v)-25 b(alue)309 b(of)f Fq(\015)57 b Fs(.)486 b(It)308 b(can)h(be)f (theoretically)h(established)g(that)27024 57088 y(these)279 b(methods)h(con)-40 b(v)-15 b(er)d(ge)281 b(asymptotically)g(to)-25 b(w)-10 b(ards)280 b(the)f(set)h(of)f(estimates)27024 58245 y(of)367 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b(e)359 b(been)h(used)f(primarily) g(to)f(solv)-15 b(e)359 b(optimal)h(\002ltering)e(prob-)27024 67499 y(lems)392 b(in)g(signal)h(processing)f(and)h(statistics.)738 b(The)-15 b(y)392 b(are)h(used)g(here)f(in)h(a)27024 68656 y(completely)435 b(dif)-25 b(ferent)434 b(frame)-25 b(w)-10 b(ork)434 b(which)h(requires)e(e)-15 b(xtensions)434 b(of)g(the)27024 69812 y(methodology)311 b(described)h(further)e(in)h (the)f(paper)-55 b(.)495 b(Broadly)310 b(speaking,)327 b(the)27024 70969 y(distrib)-20 b(utions)428 b(of)i(interest)f(are)h (approximated)h(by)f(a)f(collection)i(of)e(ran-)27024 72126 y(dom)369 b(samples)h(termed)g(particles)g(which)g(e)-25 b(v)-20 b(olv)-15 b(e)371 b(o)-15 b(v)g(er)369 b(time)h(using)g(sam-)p eop end %%Page: 2 2 TeXDict begin 2 1 bop -1953 1107 a Fs(pling)304 b(and)g(resampling)g (mechanisms.)473 b(The)304 b(population)h(of)e(samples)h(em-)-1953 2264 y(plo)-10 b(yed)337 b(by)f(our)f(method)i(mak)-10 b(es)336 b(it)g(much)g(less)f(prone)h(to)g(trapping)g(in)g(lo-)-1953 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(formulation)g(than)g(to)g(construct)f(a)h(dedicated)-1953 23633 y(sampler)347 b(for)f(a)h(particular)g(class)f(of)g(problems.)601 b(W)-80 b(e)348 b(assume)e(that)h(a)g(col-)-1953 24790 y(lection)300 b(of)e(Mark)-10 b(o)-15 b(v)299 b(k)-10 b(ernels)299 b Fp(\()p Fo(K)9957 24901 y Fl(t)10329 24790 y Fp(\))10727 24913 y Fl(t)p Fk(\025)p Fj(1)12443 24790 y Fs(with)g(in)-40 b(v)-25 b(ariant)300 b(distrib)-20 b(utions)298 b(cor)-20 b(-)-1953 25947 y(responding)290 b(to)f Fp(\()p Fq(\031)4812 26058 y Fl(t)5185 25947 y Fp(\))5583 26070 y Fl(t)p Fk(\025)p Fj(1)7289 25947 y Fs(is)g(a)-20 b(v)-25 b(ailable,)301 b(and)290 b(using)f(these)h(as)f (a)g(component)-1953 27103 y(of)343 b(the)h(proposal)f(k)-10 b(ernels)343 b(allo)-25 b(ws)343 b(the)h(e)-25 b(v)g(aluation)345 b(of)e(the)g(optimal)h(auxil-)-1953 28260 y(iary)337 b(k)-10 b(ernel.)571 b(W)-80 b(e)338 b(assume)e(that)h(good)g (importance)h(distrib)-20 b(utions)335 b(for)h(the)-1953 29417 y(conditional)370 b(probability)f(of)f(the)g(v)-25 b(ariables)369 b(being)g(mar)-18 b(ginalised)369 b(can)g(be)-1953 30574 y(sampled)253 b(from)f(and)h(e)-25 b(v)g(aluated,)255 b Fq(q)36 b Fp(\()p Fo(\001j)p Fq(\022)28 b Fp(\))p Fs(,)255 b(and)e(that)g(if)f(the)h(annealing)h(sched-)-1953 31731 y(ule)271 b(is)e(to)i(include)g(non-inte)-15 b(ger)271 b(in)-40 b(v)-15 b(erse)270 b(temperatures,)276 b(then)271 b(we)f(ha)-20 b(v)-15 b(e)272 b(ap-)-1953 32887 y(propriate)371 b(importance)g(distrib)-20 b(utions)370 b(for)g(distrib)-20 b(utions)369 b(proportional)i(to)-1953 34044 y Fq(p)p Fp(\()p Fq(z)43 b Fo(j)p Fq(\022)28 b Fp(\))667 33621 y Fl(\013)1259 34044 y Fq(;)171 b(\013)315 b Fo(2)f Fp(\(0)p Fq(;)171 b Fp(1\))p Fs(,)269 b(which)c(we)h(denote)f Fq(q)13979 34155 y Fl(\013)14569 34044 y Fp(\()p Fq(z)43 b Fo(j)p Fq(\022)28 b Fp(\))p Fs(.)357 b(W)-80 b(e)266 b(remark)f(that)g(this)-1953 35201 y(is)312 b(not)g(the)g(most)g (general)h(possible)f(approach,)329 b(b)-20 b(ut)312 b(is)f(one)i(which)g(should)-1953 36358 y(w)-10 b(ork)250 b(acceptably)h(for)d(a)i(broad)f(class)g(of)g(problems.)p -1953 36950 26121 45 v -1289 37759 a Fr(Algorithm)h(3:)309 b(A)249 b(Generic)h(Case)p -1953 38151 V -1289 38960 a Fn(Initialisation,)f(t=1:)40 40633 y Fs(Sample,)3527 39530 y Fm(n)o(\020)4821 40633 y Fq(\022)5328 40124 y Fj(\()p Fl(i)p Fj(\))5300 40887 y(1)6319 40633 y Fq(;)171 b(Z)7542 40124 y Fj(\()p Fl(i)p Fj(\))7471 40887 y(1)8533 39530 y Fm(\021)o(o)9827 39761 y Fl(N)9827 41336 y(i)p Fj(=1)11454 40633 y Fs(independently)251 b(from)e Fq(\027)64 b Fp(\()p Fo(\001)p Fp(\))40 42688 y Fs(Calculate)250 b(importance)g(weights)f Fq(W)13240 42178 y Fj(\()p Fl(i)p Fj(\))13098 42921 y Fl(t)14516 42688 y Fo(/)15729 42119 y Fl(\031)16212 42247 y Fh(1)16644 42119 y Fj(\()p Fl(\022)17378 41751 y Fh(\()p Fg(i)p Fh(\))17356 42376 y(1)18328 42119 y Fl(;Z)19182 41751 y Fh(\()p Fg(i)p Fh(\))19136 42376 y(1)20132 42119 y Fj(\))p 15729 42460 4723 43 v 15958 43284 a Fl(\027)45 b Fj(\()p Fl(\022)17150 42917 y Fh(\()p Fg(i)p Fh(\))17128 43541 y(1)18099 43284 y Fl(;Z)18953 42917 y Fh(\()p Fg(i)p Fh(\))18907 43541 y(1)19904 43284 y Fj(\))40 44351 y Fs(If)248 b(ESS)h Fq(<)g Fs(Threshold,)g(resample.) -1289 45507 y Fn(At)g(time)h Fq(t)284 b(>)h Fp(1)p Fn(:)40 47180 y Fs(Sample,)3527 46077 y Fm(n)o(\020)4821 47180 y Fq(\022)5328 46671 y Fj(\()p Fl(i)p Fj(\))5300 47414 y Fl(t)6319 47180 y Fq(;)171 b(Z)7542 46671 y Fj(\()p Fl(i)p Fj(\))7471 47414 y Fl(t)8533 46077 y Fm(\021)o(o)9827 46308 y Fl(N)9827 47883 y(i)p Fj(=1)11454 47180 y Fs(such)250 b(that)f Fo(8)p Fp(1)284 b Fo(\024)h Fq(i)g Fo(\024)g Fq(N)108 b Fs(:)1368 47925 y Fm(\020)1980 49029 y Fq(\022)2487 48520 y Fj(\()p Fl(i)p Fj(\))2459 49263 y Fl(t)3478 49029 y Fq(;)171 b(Z)4701 48520 y Fj(\()p Fl(i)p Fj(\))4630 49352 y Fl(t;)p Fj(1:)p Fk(b)p Fl(\015)6653 49492 y Fg(t)p Fi(\000)p Fh(1)7996 49352 y Fk(c)8433 47925 y Fm(\021)9329 49029 y Fo(\030)285 b(K)11189 49140 y Fl(t)p Fk(\000)p Fj(1)12777 47925 y Fm(\020)13389 49029 y Fq(\022)13896 48520 y Fj(\()p Fl(i)p Fj(\))13868 49282 y Fl(t)p Fk(\000)p Fj(1)15285 49029 y Fq(;)171 b(Z)16508 48520 y Fj(\()p Fl(i)p Fj(\))16437 49282 y Fl(t)p Fk(\000)p Fj(1)17855 49029 y Fp(;)g Fo(\001)18594 47925 y Fm(\021)1368 50684 y Fs(for)249 b Fq(j)341 b Fp(=)285 b Fo(b)p Fq(\015)5604 50795 y Fl(t)p Fk(\000)p Fj(1)7021 50684 y Fo(c)228 b Fp(+)g(1)249 b Fs(to)g Fo(b)p Fq(\015)11497 50795 y Fl(t)11869 50684 y Fo(c)p Fs(,)g Fq(Z)13590 50175 y Fj(\()p Fl(i)p Fj(\))13519 50949 y Fl(t;j)14865 50684 y Fo(\030)285 b Fq(q)36 b Fp(\()p Fo(\001j)p Fq(\022)17913 50175 y Fj(\()p Fl(i)p Fj(\))17885 50918 y Fl(t)18905 50684 y Fp(\))1368 52086 y Fs(and)250 b Fq(Z)3824 51576 y Fj(\()p Fl(i)p Fj(\))3753 52409 y Fl(t;)p Fk(d)p Fl(\015)5136 52521 y Fg(t)5503 52409 y Fk(e)6224 52086 y Fo(\030)285 b Fq(q)7763 52241 y Fl(\015)8196 52353 y Fg(t)8563 52241 y Fk(\000b)p Fl(\015)10017 52353 y Fg(t)10384 52241 y Fk(c)10820 52086 y Fp(\()p Fo(\001j)p Fq(\022)12293 51576 y Fj(\()p Fl(i)p Fj(\))12265 52319 y Fl(t)13286 52086 y Fp(\))40 53385 y Fs(Calculate)250 b(importance)g(weights)1644 54811 y Fl(W)2516 54444 y Fh(\()p Fg(i)p Fh(\))2408 55052 y Fg(t)p 1501 55136 2109 43 v 1501 55961 a Fl(W)2373 55593 y Fh(\()p Fg(i)p Fh(\))2265 56230 y Fg(t)p Fi(\000)p Fh(1)4026 55364 y Fo(/)6608 54340 y Fk(b)p Fl(\015)7422 54452 y Fg(t)7790 54340 y Fk(c)6906 54617 y Fm(Q)5107 56278 y Fl(j)39 b Fj(=)p Fk(b)p Fl(\015)6921 56418 y Fg(t)p Fi(\000)p Fh(1)8264 56278 y Fk(c)p Fj(+1)9976 54587 y Fl(p)p Fj(\()p Fl(y)24 b(;Z)12021 54220 y Fh(\()p Fg(i)p Fh(\))11975 54856 y Fg(j)12972 54587 y Fk(j)p Fl(\022)13638 54308 y Fh(\()p Fg(i)p Fh(\))14588 54587 y Fj(\))p Fl(p)p Fj(\()p Fl(y)g(;Z)16953 54220 y Fh(\()p Fg(i)p Fh(\))16907 54902 y Fi(d)p Fg(\015)17689 55052 y(t)18057 54902 y Fi(e)18481 54587 y Fk(j)p Fl(\022)19147 54308 y Fh(\()p Fg(i)p Fh(\))20097 54587 y Fj(\))20417 54308 y Fg(\015)20830 54458 y(t)21197 54308 y Fi(\000b)p Fg(\015)22579 54458 y(t)22947 54308 y Fi(c)p 9976 55136 13395 43 v 11157 55961 a Fl(q)g Fj(\()p Fl(Z)12482 55593 y Fh(\()p Fg(i)p Fh(\))12436 56230 y Fg(j)13432 55961 y Fk(j)p Fl(\022)14098 55751 y Fh(\()p Fg(i)p Fh(\))15048 55961 y Fj(\))p Fl(q)15747 56147 y Fg(\015)16160 56297 y(t)16528 56147 y Fi(\000b)p Fg(\015)17910 56297 y(t)18277 56147 y Fi(c)18702 55961 y Fj(\()p Fl(Z)19624 55593 y Fh(\()p Fg(i)p Fh(\))19578 56099 y Fg(\015)19991 56249 y(t)20574 55961 y Fk(j)p Fl(\022)21240 55751 y Fh(\()p Fg(i)p Fh(\))40 57430 y Fs(If)248 b(ESS)h Fq(<)g Fs(Threshold,)g (resample.)p -1953 57822 26121 45 v 4598 60109 a Fr(3.)598 b(EXAMPLES)249 b(AND)h(RESUL)-92 b(TS)-1953 62297 y(3.1.)598 b(T)-92 b(oy)250 b(Example)-1953 64126 y Fs(W)-80 b(e)325 b(consider)e(\002rst)g(a)h(to)-10 b(y)323 b(e)-15 b(xample)325 b(in)e(one)h(dimension.)532 b(W)-80 b(e)325 b(borro)-25 b(w)324 b(e)-15 b(x-)-1953 65283 y(ample)376 b(1)f(of)g([5])g(for)g (this)f(purpose.)687 b(The)376 b(model)f(consists)f(of)h(a)h(student) -1953 66440 y Fq(t)p Fs(-distrib)-20 b(ution)308 b(of)g(unkno)-25 b(wn)309 b(location)g(parameter)g Fq(\022)337 b Fs(with)309 b Fp(0)p Fq(:)p Fp(025)f Fs(de)-15 b(grees)-1953 67597 y(of)379 b(freedom.)699 b(F)-15 b(our)379 b(observ)-25 b(ations)379 b(are)h(a)-20 b(v)-25 b(ailable,)413 b Fq(y)568 b Fp(=)532 b(\()p Fo(\000)p Fp(20)p Fq(;)172 b Fp(1)p Fq(;)f Fp(2)p Fq(;)g Fp(3\))p Fs(.)-1953 68753 y(The)225 b(log)-5 b(arithm)226 b(of)f(the)g(mar)-18 b(ginal)226 b(lik)-10 b(elihood)226 b(in)f(this)g(instance)g(is)g(gi)-25 b(v)-15 b(en)226 b(by:)1678 71415 y Fp(log)185 b Fq(p)p Fp(\()p Fq(y)36 b Fo(j)p Fq(\022)28 b Fp(\))286 b(=)f Fo(\000)p Fp(0)p Fq(:)p Fp(525)11014 70169 y Fj(4)10478 70468 y Fm(X)10556 72569 y Fl(i)p Fj(=1)12128 71415 y Fp(log)13621 70610 y Fm(\000)14090 71415 y Fp(0)p Fq(:)p Fp(05)228 b(+)g(\()p Fq(y)18064 71526 y Fl(i)18643 71415 y Fo(\000)g Fq(\022)28 b Fp(\))20572 70936 y Fj(2)21034 70610 y Fm(\001)p 30354 44 20426 45 v 30332 1201 45 1157 v 31305 854 a Fe(N)1703 b(T)1417 b Fr(Mean)1329 b(Std.)308 b(De)-15 b(v)-70 b(.)1330 b(Min)f(Max)p 50757 1201 V 30354 1245 20426 45 v 30332 2402 45 1157 v 31268 2055 a Fs(50)1577 b(15)1425 b(1.992)2216 b(0.014)2133 b(1.95)1439 b(2.03)p 50757 2402 V 30332 3559 V 31018 3212 a(100)1329 b(15)1425 b(1.997)2216 b(0.013)2133 b(1.97)1439 b(2.04)p 50757 3559 V 30354 3603 20426 45 v 30332 4760 45 1157 v 31268 4413 a(20)1577 b(30)1425 b(1.958)2216 b(0.177)2133 b(1.09)1439 b(2.04)p 50757 4760 V 30332 5917 V 31268 5570 a(50)1577 b(30)1425 b(1.997)2216 b(0.008)2133 b(1.98)1439 b(2.01)p 50757 5917 V 30332 7073 V 31018 6726 a(100)1329 b(30)1425 b(1.997)2216 b(0.007)2133 b(1.98)1439 b(2.01)p 50757 7073 V 30354 7118 20426 45 v 30332 8274 45 1157 v 31268 7927 a(20)1577 b(60)1425 b(1.998)2216 b(0.015)2133 b(1.91)1439 b(2.02)p 50757 8274 V 30332 9431 V 31268 9084 a(50)1577 b(60)1425 b(1.997)2216 b(0.005)2133 b(1.99)1439 b(2.01)p 50757 9431 V 30354 9476 20426 45 v 27024 11380 a Fr(T)-92 b(able)372 b(1)p Fs(.)677 b(Simulation)373 b(results)e(for)g(the)i(to)-10 b(y)372 b(problem.)678 b(Each)372 b(line)h(sum-)27024 12536 y(marises)379 b(50)i(simulations)f (with)h Fq(N)487 b Fs(particles)381 b(and)g(\002nal)f(temperature)i Fq(T)142 b Fs(.)27024 13693 y(Only)249 b(one)h(simulation)f(f)-10 b(ailed)250 b(to)f(\002nd)g(the)h(correct)f(mode.)27024 17295 y(which)283 b(is)f(not)h(susceptible)g(to)g(analytic)h (maximisation.)411 b(Ho)-25 b(we)g(v)-15 b(er)-40 b(,)293 b(global)27024 18452 y(maximum)219 b(is)f(kno)-25 b(wn)220 b(to)e(be)h(located)h(at)f Fp(1)p Fq(:)p Fp(997)p Fs(,)225 b(and)219 b(local)h(maxima)f(e)-15 b(xist)219 b(at)27024 19609 y Fo(f\000)p Fp(19)p Fq(:)p Fp(993)p Fq(;)171 b Fp(1)p Fq(:)p Fp(086)p Fq(;)h Fp(2)p Fq(:)p Fp(906)p Fo(g)p Fs(.)508 b(W)-80 b(e)317 b(can)f(complete)g(this)f(model)i(by)e (consid-)27024 20765 y(ering)296 b(the)g(student)h Fq(t)p Fs(-distrib)-20 b(ution)295 b(as)h(a)g(scale-mixture)h(of)f(Gaussians)g (and)27024 21922 y(associating)394 b(a)h(latent)g(v)-25 b(ariance)395 b(parameter)g Fq(Z)44107 22033 y Fl(i)44853 21922 y Fs(with)f(each)i(observ)-25 b(ation.)27024 23079 y(The)249 b(log)g(lik)-10 b(elihood)250 b(is)f(then:)27347 26228 y Fp(log)185 b Fq(p)p Fp(\()p Fq(y)36 b(;)171 b(z)43 b Fo(j)p Fq(\022)28 b Fp(\))286 b(=)f Fo(\000)35326 24983 y Fj(4)34789 25282 y Fm(X)34867 27382 y Fl(i)p Fj(=1)36439 25424 y Fm(\002)36866 26228 y Fp(0)p Fq(:)p Fp(475)171 b(log)185 b Fq(z)41338 26339 y Fl(i)41917 26228 y Fp(+)228 b(0)p Fq(:)p Fp(025)p Fq(z)45749 26339 y Fl(i)46328 26228 y Fp(+)g(0)p Fq(:)p Fp(5)p Fq(z)49136 26339 y Fl(i)49488 26228 y Fp(\()p Fq(y)50390 26339 y Fl(i)50969 26228 y Fo(\000)g Fq(\022)28 b Fp(\))52898 25750 y Fj(2)53360 25424 y Fm(\003)28684 29355 y Fs(In)228 b(the)g(interest)g(of)f (simplicity)-65 b(,)232 b(we)d(mak)-10 b(e)229 b(use)e(of)h(a)g(linear) g(temperature)27024 30512 y(scale,)356 b Fq(\015)30149 30623 y Fl(t)30968 30512 y Fp(=)447 b Fq(t)p Fs(,)356 b(which)335 b(tak)-10 b(es)335 b(only)f(inte)-15 b(ger)335 b(v)-25 b(alues.)566 b(As)334 b(we)h(are)g(able)g(to)27024 31668 y(e)-25 b(v)g(aluate)246 b(the)f(mar)-18 b(ginal)245 b(lik)-10 b(elihood)245 b(function)g(pointwise,)h(and)g(can)f(sample) 27024 32825 y(from)j(the)i(conditional)g(distrib)-20 b(utions)28366 35669 y Fq(\031)28952 35780 y Fl(t)29324 35669 y Fp(\()p Fq(z)30198 35780 y Fj(1:)p Fl(\015)31271 35892 y Fg(t)31693 35669 y Fo(j)p Fq(\022)28 b(;)173 b(y)36 b Fp(\))284 b(=)35505 34383 y Fl(\015)35938 34495 y Fg(t)35251 34722 y Fm(Y)35244 36823 y Fl(i)p Fj(=1)36738 35669 y Fo(G)58 b Fq(a)38118 34266 y Fm(\022)38871 35669 y Fq(z)39347 35780 y Fl(i)39870 34224 y Fm(\014)39870 34822 y(\014)39870 35420 y(\014)39870 36017 y(\014)40211 35669 y Fp(0)p Fq(:)p Fp(525)p Fq(;)171 b Fp(0)p Fq(:)p Fp(025)228 b(+)46715 35023 y(\()p Fq(y)47617 35134 y Fl(i)48196 35023 y Fo(\000)g Fq(\022)28 b Fp(\))50125 34600 y Fj(2)p 46715 35441 3873 43 v 48395 36344 a Fp(2)50853 34266 y Fm(\023)52949 35669 y Fs(\(5\))29361 38522 y Fq(\031)29947 38633 y Fl(t)30319 38522 y Fp(\()p Fq(\022)g Fo(j)p Fq(z)31984 38633 y Fj(1:)p Fl(\015)33057 38745 y Fg(t)33481 38522 y Fp(\))284 b Fo(/)h(N)36401 37418 y Fm(\020)37013 38522 y Fq(\022)37691 37376 y Fm(\014)37691 37974 y(\014)37691 38572 y(\014)38032 38522 y Fq(\026)38649 38013 y Fj(\()p Fl(\022)22 b Fj(\))38649 38756 y Fl(t)39758 38522 y Fq(;)171 b Fp(\006)40953 38013 y Fj(\()p Fl(\022)22 b Fj(\))40953 38756 y Fl(t)42194 37418 y Fm(\021)52949 38522 y Fs(\(6\))27024 40999 y(where)250 b(the)f(parameters)28654 44302 y Fp(\006)29394 43793 y Fj(\()p Fl(\022)22 b Fj(\))29394 44536 y Fl(t)30786 44302 y Fp(=)31867 42601 y Fm(")33045 43057 y Fl(t)32464 43356 y Fm(X)32542 45456 y Fl(i)p Fj(=1)34651 43057 y(4)34114 43356 y Fm(X)34151 45456 y Fl(j)39 b Fj(=1)35764 44302 y Fq(z)36240 44413 y Fl(i;j)37222 42601 y Fm(#)37819 42792 y Fk(\000)p Fj(1)40381 44302 y Fp(=)41462 42601 y Fm(")42060 44302 y Fp(1)p Fq(=)p Fp(\006)43824 43793 y Fj(\()p Fl(\022)22 b Fj(\))43824 44555 y Fl(t)p Fk(\000)p Fj(1)45468 44302 y Fp(+)47029 43057 y Fj(4)46492 43356 y Fm(X)46529 45456 y Fl(j)39 b Fj(=1)48142 44302 y Fq(z)48618 44413 y Fl(t;j)49620 42601 y Fm(#)50218 42792 y Fk(\000)p Fj(1)52949 44302 y Fs(\(7\))28776 47904 y Fq(\026)29393 47394 y Fj(\()p Fl(\022)22 b Fj(\))29393 48137 y Fl(t)30786 47904 y Fp(=)285 b(\006)32607 47394 y Fj(\()p Fl(\022)22 b Fj(\))32607 48137 y Fl(t)34467 46658 y(t)33886 46957 y Fm(X)33964 49058 y Fl(i)p Fj(=1)35535 47904 y Fq(y)36075 47425 y Fl(T)36724 47904 y Fq(z)37200 48015 y Fl(i)38920 47904 y Fp(=)284 b(\006)40740 47394 y Fj(\()p Fl(\026)p Fj(\))40740 48137 y Fl(t)42104 46800 y Fm(\020)42715 47904 y Fq(\026)43332 47394 y Fj(\()p Fl(\022)22 b Fj(\))43332 48157 y Fl(t)p Fk(\000)p Fj(1)44750 47904 y Fq(=)p Fp(\006)46002 47394 y Fj(\()p Fl(\022)g Fj(\))46002 48157 y Fl(t)p Fk(\000)p Fj(1)47646 47904 y Fp(+)228 b Fq(y)49210 47425 y Fl(T)49859 47904 y Fq(z)50335 48015 y Fl(t)50707 46800 y Fm(\021)52949 47904 y Fs(\(8\))27024 50997 y(may)393 b(be)g(obtained)g(recursi)-25 b(v)-15 b(ely)-65 b(.)740 b(Consequently)-65 b(,)429 b(we)393 b(can)g(mak)-10 b(e)394 b(use)e(of)27024 52154 y(algorithm)427 b(2)g(to)g(solv)-15 b(e)427 b(this)f(problem.)843 b(W)-80 b(e)428 b(use)f(an)g(instrumental)g(uni-)27024 53311 y(form)363 b Fp([)p Fo(\000)p Fp(50)p Fq(;)172 b Fp(50])363 b Fs(prior)g(distrib)-20 b(ution)363 b(o)-15 b(v)g(er)364 b Fq(\022)28 b Fs(.)653 b(Some)364 b(simulation)f(results) 27024 54468 y(are)350 b(gi)-25 b(v)-15 b(en)350 b(in)g(table)g(1.)611 b(The)350 b(estimate)g(is)f(tak)-10 b(en)351 b(to)f(be)g(the)g(\002rst) f(moment)27024 55624 y(of)281 b(the)h(empirical)h(distrib)-20 b(ution)281 b(induced)i(by)f(the)g(\002nal)g(particle)g(ensemble;)27024 56781 y(this)295 b(may)h(be)g(justi\002ed)g(by)g(the)g(asymptotic)h (\(in)e(the)h(in)-40 b(v)-15 b(erse)296 b(temperature\))27024 57938 y(normality)249 b(of)g(the)h(tar)-18 b(get)249 b(distrib)-20 b(ution)249 b(\(see,)g(for)g(e)-15 b(xample,)250 b([2,)f(p.)309 b(203]\).)27024 60717 y Fr(3.2.)598 b(Stochastic)249 b(V)-100 b(olatility)27024 62605 y Fs(W)-80 b(e)280 b(tak)-10 b(e)279 b(this)g(more)g(comple)-15 b(x)280 b(e)-15 b(xample)281 b(from)e([4)o(].)399 b(W)-80 b(e)280 b(consider)f(the)h(fol-)27024 63762 y(lo)-25 b(wing)249 b(model:)30231 65958 y Fq(Z)30928 66069 y Fl(i)31564 65958 y Fp(=)284 b Fq(\013)229 b Fp(+)f Fq(\016)38 b(Z)35742 66069 y Fl(i)p Fk(\000)p Fj(1)37365 65958 y Fp(+)228 b Fq(\033)38974 66069 y Fl(u)39520 65958 y Fq(u)40109 66069 y Fl(i)43668 65958 y Fq(Z)44365 66069 y Fj(1)45110 65958 y Fo(\030)285 b(N)47348 65153 y Fm(\000)47818 65958 y Fq(\026)48435 66069 y Fj(0)48896 65958 y Fq(;)171 b(\033)49972 65479 y Fj(2)49936 66133 y(0)50433 65153 y Fm(\001)52949 65958 y Fs(\(9\))30334 68194 y Fq(Y)30928 68305 y Fl(i)31564 68194 y Fp(=)284 b(exp)34380 66791 y Fm(\022)35266 67549 y Fq(Z)35963 67660 y Fl(i)p 35266 67966 1048 43 v 35534 68869 a Fp(2)36447 66791 y Fm(\023)37371 68194 y Fq(\017)37786 68305 y Fl(i)52450 68194 y Fs(\(10\))27024 70969 y(where)250 b Fq(u)30296 71080 y Fl(i)30898 70969 y Fs(and)h Fq(\017)33002 71080 y Fl(i)33603 70969 y Fs(are)f (uncorrelated)h(standard)g(normal)f(random)h(v)-25 b(ariables,)27024 72126 y(and)349 b Fq(\022)502 b Fp(=)474 b(\()p Fq(\013)q(;)171 b(\016)-19 b(;)171 b(\033)34047 72237 y Fl(u)34592 72126 y Fp(\))p Fs(.)607 b(The)349 b(mar)-18 b(ginal)349 b(lik)-10 b(elihood)349 b(of)f(interest)h Fq(p)p Fp(\()p Fq(\022)28 b Fo(j)p Fq(y)36 b Fp(\))350 b Fs(is)p eop end %%Page: 4 4 TeXDict begin 4 3 bop -1953 0 a currentpoint currentpoint translate 0.32166 0.32166 scale neg exch neg exch translate -1953 0 a -1953 0 a gsave currentpoint currentpoint translate 270 neg rotate neg exch neg exch translate -1953 0 a @beginspecial 50 @llx 50 @lly 554 @urx 770 @ury 5040 @rwi @setspecial %%BeginDocument: mml_convergence2.eps %!PS-Adobe-2.0 %%Title: mml_convergence2.eps %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Thu Oct 20 16:40:02 2005 %%DocumentFonts: (atend) %%BoundingBox: 50 50 554 770 %%Orientation: Landscape %%Pages: (atend) %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 M 0 PFs V } for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 2 1 roll M PFs 0 V } for } if stroke grestore } def % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def end %%EndProlog %%Page: 1 1 gnudict begin gsave 50 50 translate 0.100 0.100 scale 90 rotate 0 -5040 translate 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 714 420 M 63 0 V 6185 0 R -63 0 V stroke 630 420 M [ [(Helvetica) 140.0 0.0 true true 0 (-1.5)] ] -46.7 MRshow 1.000 UL LTb 714 1260 M 63 0 V 6185 0 R -63 0 V stroke 630 1260 M [ [(Helvetica) 140.0 0.0 true true 0 (-1)] ] -46.7 MRshow 1.000 UL LTb 714 2100 M 63 0 V 6185 0 R -63 0 V stroke 630 2100 M [ [(Helvetica) 140.0 0.0 true true 0 (-0.5)] ] -46.7 MRshow 1.000 UL LTb 714 2940 M 63 0 V 6185 0 R -63 0 V stroke 630 2940 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb 714 3780 M 63 0 V 6185 0 R -63 0 V stroke 630 3780 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.5)] ] -46.7 MRshow 1.000 UL LTb 714 4620 M 63 0 V 6185 0 R -63 0 V stroke 630 4620 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1)] ] -46.7 MRshow 1.000 UL LTb 714 420 M 0 63 V 0 4137 R 0 -63 V stroke 714 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MCshow 1.000 UL LTb 1495 420 M 0 63 V 0 4137 R 0 -63 V stroke 1495 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.5)] ] -46.7 MCshow 1.000 UL LTb 2276 420 M 0 63 V 0 4137 R 0 -63 V stroke 2276 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1)] ] -46.7 MCshow 1.000 UL LTb 3057 420 M 0 63 V 0 4137 R 0 -63 V stroke 3057 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1.5)] ] -46.7 MCshow 1.000 UL LTb 3838 420 M 0 63 V 0 4137 R 0 -63 V stroke 3838 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 2)] ] -46.7 MCshow 1.000 UL LTb 4619 420 M 0 63 V 0 4137 R 0 -63 V stroke 4619 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 2.5)] ] -46.7 MCshow 1.000 UL LTb 5400 420 M 0 63 V 0 4137 R 0 -63 V stroke 5400 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 3)] ] -46.7 MCshow 1.000 UL LTb 6181 420 M 0 63 V 0 4137 R 0 -63 V stroke 6181 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 3.5)] ] -46.7 MCshow 1.000 UL LTb 6962 420 M 0 63 V 0 4137 R 0 -63 V stroke 6962 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 4)] ] -46.7 MCshow 1.000 UL LTb 1.000 UL LTb 714 420 M 6248 0 V 0 4200 V -6248 0 V 714 420 L LTb 140 2520 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true true 0 (Particle System Estimates)] ] -46.7 MCshow grestore LTb 3838 70 M [ [(Helvetica) 140.0 0.0 true true 0 (Inverse Temperature)] ] -46.7 MCshow LTb 3838 4830 M [ [(Helvetica) 140.0 0.0 true true 0 (Convergence of the Algorithm)] ] -46.7 MCshow 1.000 UP 1.000 UL LT0 LTb 6311 4487 M [ [(Symbol) 140.0 0.0 true true 0 (a)] ] -46.7 MRshow LT0 6395 4487 M 399 0 V 739 2176 M 6 -480 V 6 -21 V 7 -55 V 6 -133 V 6 95 V 6 -134 V 7 10 V 6 -18 V 6 -116 V 6 -132 V 7 -251 V 6 168 V 6 -46 V 6 165 V 7 -159 V 6 58 V 6 53 V 6 -26 V 7 157 V 6 29 V 6 -87 V 6 223 V 7 138 V 6 -11 V 6 -125 V 6 226 V 7 69 V 6 74 V 6 82 V 6 -62 V 7 123 V 6 101 V 6 57 V 6 157 V 7 -327 V 6 163 V 6 18 V 6 31 V 7 33 V 6 36 V 6 -45 V 6 -16 V 7 89 V 6 11 V 6 31 V 6 -57 V 7 20 V 6 -21 V 6 -85 V 6 13 V 7 -60 V 6 3 V 6 5 V 6 48 V 7 -26 V 6 -75 V 12 138 V 13 3 V 12 11 V 13 47 V 12 -82 V 13 146 V 12 -60 V 13 5 V 12 -136 V 13 98 V 12 -40 V 13 35 V 12 -65 V 13 263 V 12 -49 V 13 -7 V 12 -56 V 13 126 V 12 -82 V 13 15 V 12 -24 V 13 73 V 12 71 V 13 -20 V 12 -108 V 13 -10 V 12 2 V 13 87 V 12 129 V 13 -138 V 12 110 V 13 -31 V 12 5 V 13 66 V 12 -42 V 13 16 V 12 32 V 13 -29 V 12 38 V 13 -9 V 12 101 V 13 -28 V 12 -9 V 13 -29 V 12 -27 V 13 14 V stroke 1664 2644 M 12 -15 V 13 -36 V 12 78 V 13 -36 V 12 -48 V 13 31 V 12 -19 V 13 70 V 12 -11 V 13 0 V 12 -12 V 13 0 V 12 -32 V 13 23 V 12 -24 V 13 1 V 12 -42 V 13 22 V 12 28 V 13 -25 V 12 -20 V 13 11 V 12 -16 V 13 31 V 12 -18 V 19 33 V 19 46 V 18 -40 V 19 -20 V 19 -7 V 19 31 V 18 14 V 19 -15 V 19 -6 V 19 19 V 18 -22 V 19 -26 V 19 -2 V 19 19 V 18 -11 V 19 -73 V 19 65 V 18 -45 V 19 0 V 19 18 V 19 -1 V 18 -5 V 19 40 V 19 -53 V 19 -15 V 18 1 V 19 1 V 19 37 V 19 -17 V 18 36 V 19 -23 V 19 54 V 19 -37 V 18 -39 V 19 -17 V 19 12 V 19 11 V 18 -2 V 19 -4 V 19 -53 V 19 60 V 18 -13 V 19 -22 V 19 47 V 19 -5 V 18 6 V 19 32 V 19 6 V 19 -31 V 18 -38 V 19 65 V 19 -25 V 19 -30 V 18 29 V 19 50 V 19 -17 V 19 43 V 18 -32 V 19 23 V 19 -10 V 18 -25 V 19 36 V 19 32 V 19 12 V 18 -10 V 19 -35 V 25 -10 V 19 -1 V 19 2 V 18 -14 V 19 25 V 19 -7 V 19 -17 V 18 8 V 19 -19 V 19 21 V 19 -26 V 18 6 V 19 10 V stroke 3463 2615 M 19 -14 V 19 14 V 18 -19 V 19 1 V 19 -13 V 19 -5 V 18 48 V 19 -37 V 19 12 V 19 -10 V 18 30 V 19 -8 V 19 9 V 19 -12 V 18 -29 V 19 -15 V 19 -16 V 19 -35 V 18 -1 V 19 -32 V 12 33 V 25 -4 V 25 25 V 25 2 V 25 16 V 25 -48 V 25 21 V 25 -42 V 25 21 V 25 12 V 25 35 V 25 8 V 25 14 V 25 -17 V 25 3 V 25 3 V 25 -46 V 25 24 V 25 29 V 25 -3 V 25 6 V 25 -21 V 25 45 V 25 -12 V 25 1 V 25 2 V 25 -20 V 25 -3 V 25 6 V 25 25 V 25 8 V 25 -8 V 25 21 V 25 -39 V 25 7 V 25 31 V 25 -4 V 25 8 V 25 -27 V 25 9 V 25 -8 V 25 -2 V 25 -10 V 25 0 V 25 2 V 25 22 V 25 -4 V 25 4 V 25 -3 V 25 -11 V 25 25 V 25 0 V 25 -37 V 25 23 V 25 -9 V 25 0 V 25 26 V 25 -19 V 25 -4 V 25 -5 V 25 11 V 25 -24 V 25 13 V 31 -9 V 31 0 V 32 -27 V 31 -3 V 31 -10 V 31 24 V 32 -1 V 31 -30 V 31 8 V 31 3 V 32 -8 V 31 -28 V 31 20 V 31 -2 V 32 -3 V 31 6 V 31 12 V 31 20 V 32 0 V 31 -12 V 31 12 V stroke 6056 2566 M 31 -21 V 32 13 V 31 7 V 31 -4 V 31 -34 V 31 20 V 32 33 V 31 -1 V 31 -27 V 31 -17 V 32 13 V 31 -1 V 31 10 V 31 -4 V 32 -21 V 31 -18 V 31 26 V 31 3 V 32 4 V 31 -6 V 31 -21 V 31 -3 V 32 34 V 31 24 V 31 -15 V 31 -46 V 32 -11 V 31 -6 V 31 25 V 1.000 UL LT1 LTb 6311 4347 M [ [(Symbol) 140.0 0.0 true true 0 (d)] ] -46.7 MRshow LT1 6395 4347 M 399 0 V 739 4393 M 6 -36 V 6 21 V 7 1 V 6 -19 V 6 28 V 6 -14 V 7 -1 V 6 -1 V 6 -14 V 6 -14 V 7 -34 V 6 36 V 6 -14 V 6 29 V 7 -23 V 6 16 V 6 7 V 6 1 V 7 29 V 6 5 V 6 -6 V 6 33 V 7 28 V 6 -8 V 6 -15 V 6 32 V 7 15 V 6 14 V 6 12 V 6 -6 V 7 15 V 6 17 V 6 9 V 6 20 V 7 -44 V 6 22 V 6 2 V 6 4 V 7 5 V 6 6 V 6 -8 V 6 1 V 7 11 V 6 4 V 6 4 V 6 -9 V 7 3 V 6 -2 V 6 -16 V 6 4 V 7 -7 V 6 -1 V 6 2 V 6 5 V 7 -2 V 6 -12 V 12 18 V 13 -2 V 12 2 V 13 4 V 12 -9 V 13 18 V 12 -9 V 13 0 V 12 -15 V 13 7 V 12 -7 V 13 2 V 12 -7 V 13 29 V 12 -6 V 13 -1 V 12 -5 V 13 13 V 12 -8 V 13 0 V 12 -1 V 13 8 V 12 7 V 13 -2 V 12 -12 V 13 -1 V 12 1 V 13 9 V 12 14 V 13 -15 V 12 12 V 13 -4 V 12 1 V 13 9 V 12 -6 V 13 2 V 12 4 V 13 -4 V 12 5 V 13 -1 V 12 12 V 13 -4 V 12 0 V 13 -4 V 12 -3 V 13 2 V stroke 1664 4581 M 12 -1 V 13 -4 V 12 8 V 13 -5 V 12 -5 V 13 5 V 12 -5 V 13 10 V 12 -1 V 13 0 V 12 0 V 13 0 V 12 -5 V 13 4 V 12 -3 V 13 -1 V 12 -5 V 13 5 V 12 2 V 13 -3 V 12 -2 V 13 1 V 12 -2 V 13 4 V 12 -3 V 19 4 V 19 3 V 18 -3 V 19 -2 V 19 -2 V 19 5 V 18 0 V 19 -2 V 19 0 V 19 2 V 18 -2 V 19 -3 V 19 1 V 19 3 V 18 -1 V 19 -9 V 19 7 V 18 -6 V 19 0 V 19 2 V 19 0 V 18 0 V 19 5 V 19 -7 V 19 -1 V 18 1 V 19 0 V 19 5 V 19 -2 V 18 5 V 19 -3 V 19 7 V 19 -5 V 18 -4 V 19 -2 V 19 0 V 19 2 V 18 -1 V 19 0 V 19 -6 V 19 7 V 18 -2 V 19 -3 V 19 5 V 19 -1 V 18 1 V 19 5 V 19 0 V 19 -4 V 18 -5 V 19 8 V 19 -3 V 19 -3 V 18 3 V 19 6 V 19 -3 V 19 6 V 18 -4 V 19 3 V 19 -2 V 18 -3 V 19 5 V 19 4 V 19 1 V 18 -1 V 19 -4 V 25 -1 V 19 -1 V 19 0 V 18 -1 V 19 3 V 19 -1 V 19 -2 V 18 1 V 19 -2 V 19 3 V 19 -4 V 18 1 V 19 1 V stroke 3463 4579 M 19 -1 V 19 1 V 18 -2 V 19 0 V 19 -2 V 19 -1 V 18 6 V 19 -5 V 19 2 V 19 -1 V 18 3 V 19 -1 V 19 2 V 19 -2 V 18 -3 V 19 -2 V 19 -2 V 19 -5 V 18 1 V 19 -4 V 12 4 V 25 0 V 25 3 V 25 0 V 25 1 V 25 -5 V 25 3 V 25 -5 V 25 3 V 25 3 V 25 3 V 25 1 V 25 2 V 25 -2 V 25 0 V 25 1 V 25 -5 V 25 2 V 25 4 V 25 -1 V 25 1 V 25 -4 V 25 6 V 25 -2 V 25 1 V 25 0 V 25 -3 V 25 0 V 25 1 V 25 2 V 25 1 V 25 0 V 25 2 V 25 -5 V 25 1 V 25 4 V 25 -1 V 25 1 V 25 -3 V 25 1 V 25 -1 V 25 0 V 25 -2 V 25 1 V 25 0 V 25 3 V 25 0 V 25 1 V 25 -1 V 25 -1 V 25 3 V 25 0 V 25 -6 V 25 3 V 25 -1 V 25 0 V 25 4 V 25 -3 V 25 -1 V 25 0 V 25 1 V 25 -2 V 25 2 V 31 -2 V 31 0 V 32 -3 V 31 0 V 31 -2 V 31 3 V 32 1 V 31 -5 V 31 2 V 31 1 V 32 -1 V 31 -4 V 31 3 V 31 -1 V 32 0 V 31 0 V 31 1 V 31 3 V 32 0 V 31 -2 V 31 2 V stroke 6056 4574 M 31 -3 V 32 2 V 31 0 V 31 0 V 31 -4 V 31 3 V 32 3 V 31 0 V 31 -4 V 31 -2 V 32 3 V 31 -1 V 31 1 V 31 0 V 32 -3 V 31 -2 V 31 4 V 31 0 V 32 1 V 31 -2 V 31 -2 V 31 -1 V 32 5 V 31 2 V 31 -2 V 31 -5 V 32 -1 V 31 -1 V 31 4 V 1.000 UL LT2 LTb 6311 4207 M [ [(Symbol) 140.0 0.0 true true 0 (s)] ] -46.7 MRshow LT2 6395 4207 M 399 0 V -6055 4 R 6 -382 V 6 182 V 7 -262 V 6 -156 V 6 -42 V 6 -7 V 7 -51 V 6 7 V 6 -16 V 6 -11 V 7 -11 V 6 39 V 6 -43 V 6 3 V 7 7 V 6 0 V 6 -7 V 6 -4 V 7 5 V 6 18 V 6 13 V 6 46 V 7 6 V 6 -42 V 6 -16 V 6 -2 V 7 16 V 6 9 V 6 23 V 6 -12 V 7 -2 V 6 -11 V 6 -30 V 6 1 V 7 8 V 6 -5 V 6 -6 V 6 -17 V 7 0 V 6 12 V 6 -17 V 6 -10 V 7 -3 V 6 5 V 6 1 V 6 -31 V 7 3 V 6 -3 V 6 -3 V 6 -4 V 7 -6 V 6 16 V 6 -3 V 6 -3 V 7 -8 V 6 17 V 12 -25 V 13 -22 V 12 37 V 13 -22 V 12 -45 V 13 -2 V 12 9 V 13 35 V 12 46 V 13 124 V 12 16 V 13 -2 V 12 10 V 13 3 V 12 -9 V 13 -14 V 12 -2 V 13 -9 V 12 -1 V 13 -3 V 12 2 V 13 -8 V 12 -18 V 13 5 V 12 -5 V 13 4 V 12 -14 V 13 -9 V 12 10 V 13 3 V 12 -11 V 13 -11 V 12 -10 V 13 -7 V 12 3 V 13 -14 V 12 -7 V 13 -7 V 12 0 V 13 -4 V 12 -6 V 13 -10 V 12 1 V 13 -7 V 12 8 V 13 0 V stroke 1664 3434 M 12 -3 V 13 1 V 12 -8 V 13 1 V 12 -8 V 13 -5 V 12 -12 V 13 1 V 12 1 V 13 -1 V 12 -2 V 13 26 V 12 -19 V 13 2 V 12 6 V 13 0 V 12 0 V 13 5 V 12 6 V 13 -6 V 12 1 V 13 -4 V 12 -1 V 13 -6 V 12 10 V 19 -8 V 19 3 V 18 -1 V 19 -1 V 19 2 V 19 3 V 18 -8 V 19 4 V 19 -6 V 19 -4 V 18 5 V 19 2 V 19 6 V 19 1 V 18 -1 V 19 8 V 19 6 V 18 2 V 19 -9 V 19 -1 V 19 -1 V 18 -2 V 19 -12 V 19 5 V 19 4 V 18 -4 V 19 14 V 19 -10 V 19 0 V 18 4 V 19 3 V 19 2 V 19 -1 V 18 8 V 19 -3 V 19 -5 V 19 -3 V 18 7 V 19 -1 V 19 3 V 19 -9 V 18 3 V 19 3 V 19 -7 V 19 9 V 18 0 V 19 4 V 19 -2 V 19 4 V 18 -1 V 19 -9 V 19 0 V 19 10 V 18 -11 V 19 6 V 19 -6 V 19 2 V 18 0 V 19 0 V 19 1 V 18 -1 V 19 -8 V 19 0 V 19 -1 V 18 2 V 19 2 V 25 -2 V 19 -4 V 19 4 V 18 2 V 19 -3 V 19 -3 V 19 10 V 18 0 V 19 -5 V 19 1 V 19 -6 V 18 6 V 19 0 V stroke 3463 3421 M 19 -4 V 19 3 V 18 -4 V 19 -1 V 19 -1 V 19 12 V 18 0 V 19 -6 V 19 -5 V 19 6 V 18 -2 V 19 1 V 19 -10 V 19 3 V 18 14 V 19 13 V 19 12 V 19 13 V 18 1 V 19 -15 V 12 -4 V 25 9 V 25 1 V 25 3 V 25 -4 V 25 -4 V 25 -1 V 25 -5 V 25 4 V 25 5 V 25 -18 V 25 0 V 25 -3 V 25 -2 V 25 -1 V 25 -4 V 25 3 V 25 -8 V 25 0 V 25 4 V 25 4 V 25 4 V 25 3 V 25 1 V 25 -2 V 25 3 V 25 -4 V 25 -4 V 25 -1 V 25 8 V 25 0 V 25 -1 V 25 -1 V 25 6 V 25 3 V 25 4 V 25 1 V 25 -5 V 25 2 V 25 -3 V 25 -2 V 25 -4 V 25 6 V 25 1 V 25 -11 V 25 -3 V 25 -5 V 25 0 V 25 -8 V 25 2 V 25 -4 V 25 2 V 25 6 V 25 3 V 25 -1 V 25 0 V 25 -1 V 25 6 V 25 -1 V 25 -5 V 25 6 V 25 -1 V 25 0 V 31 6 V 31 -4 V 32 1 V 31 9 V 31 4 V 31 1 V 32 5 V 31 5 V 31 2 V 31 2 V 32 -4 V 31 2 V 31 3 V 31 -2 V 32 -1 V 31 0 V 31 1 V 31 12 V 32 -3 V 31 -1 V 31 -1 V stroke 6056 3467 M 31 5 V 32 -4 V 31 4 V 31 1 V 31 -2 V 31 -1 V 32 5 V 31 -4 V 31 8 V 31 1 V 32 0 V 31 2 V 31 1 V 31 2 V 32 -5 V 31 1 V 31 -7 V 31 0 V 32 -5 V 31 0 V 31 0 V 31 -2 V 32 1 V 31 5 V 31 1 V 31 5 V 32 -1 V 31 -1 V 31 -1 V 1.000 UL LTb 714 420 M 6248 0 V 0 4200 V -6248 0 V 714 420 L 1.000 UP stroke grestore end showpage %%Trailer %%DocumentFonts: Symbol Helvetica %%Pages: 1 %%EndDocument @endspecial 54047 0 a currentpoint grestore moveto 54047 0 a -1953 0 a currentpoint currentpoint translate 1 0.32166 div 1 0.32166 div scale neg exch neg exch translate -1953 0 a 19917 x Fr(Fig)-15 b(.)246 b(1)p Fs(.)308 b(P)-15 b(arameter)247 b(estimates)e(as)h(a)g(function)h(of)e(the)h(in)-40 b(v)-15 b(erse)247 b(temperature.)-1953 23470 y(a)-20 b(v)-25 b(ailable)381 b(only)f(as)f(a)h(high)f(dimensional)h(inte)-15 b(gral)380 b(o)-15 b(v)g(er)380 b(the)g(latent)g(v)-25 b(ari-)-1953 24627 y(ables,)250 b Fq(Z)319 b Fs(and)250 b(this)f(inte)-15 b(gral)249 b(cannot)h(be)g(computed.)-292 25792 y(In)228 b(this)f(case)i(we)f(are)h(unable)f(to)h(use)e (algorithm)i(2,)j(and)d(emplo)-10 b(y)229 b(a)f(v)-25 b(ari-)-1953 26949 y(ant)362 b(of)f(algorithm)h(3.)646 b(The)362 b(serial)f(nature)h(of)g(the)g(observ)-25 b(ation)362 b(sequence)-1953 28105 y(suggests)217 b(introducing)h(blocks)g(of)g (the)g(latent)g(v)-25 b(ariable)219 b(at)f(each)g(time,)225 b(rather)-1953 29262 y(than)268 b(replicating)g(the)g(entire)g(set)f (at)g(each)i(iteration.)364 b(This)266 b(is)h(moti)-25 b(v)g(ated)269 b(by)-1953 30419 y(the)228 b(same)f(considerations)h(as) f(the)g(pre)-25 b(viously)227 b(discussed)g(sequence)i(of)d(dis-)-1953 31576 y(trib)-20 b(utions,)380 b(b)-20 b(ut)353 b(mak)-10 b(es)354 b(use)g(of)f(the)h(structure)g(of)f(this)g(particular)h (model.)-1953 32733 y(Thus,)269 b(at)c(time)h Fq(t)p Fs(,)j(gi)-25 b(v)-15 b(en)266 b(a)f(set)g(of)g Fq(M)373 b Fs(observ)-25 b(ations,)269 b(we)d(ha)-20 b(v)-15 b(e)266 b(a)g(sample)f(of)-1953 33889 y Fq(M)108 b(\015)-327 34000 y Fl(t)289 33889 y Fs(v)-20 b(olatilities,)246 b Fo(b)p Fq(\015)5955 34000 y Fl(t)6327 33889 y Fo(c)e Fs(complete)h(sets)f(and)h Fq(M)108 b Fp(\()p Fq(\015)16368 34000 y Fl(t)16949 33889 y Fo(\000)209 b(b)p Fq(\015)18938 34000 y Fl(t)19310 33889 y Fo(c)p Fp(\))245 b Fs(which)g(com-)-1953 35046 y(prise)329 b(a)h(partial)g(estimate)g(of)f(another)i(replicate.) 551 b(That)330 b(is,)349 b(we)330 b(use)f(tar)-18 b(get)-1953 36203 y(distrib)e(utions)249 b(of)g(this)f(form:)-1087 39223 y Fq(p)-573 39334 y Fl(t)-201 39223 y Fp(\()p Fq(\013)q(;)172 b(\016)-19 b(;)170 b(\033)-21 b(;)172 b(z)3695 39334 y Fl(t)4067 39223 y Fp(\))285 b Fo(/)p Fq(p)171 b Fp(\()p Fq(\013)q(;)g(\016)-19 b(;)171 b(\033)36 b Fp(\))9821 37900 y Fk(b)p Fl(\015)10635 38012 y Fg(t)11003 37900 y Fk(c)9948 38276 y Fm(Y)9941 40377 y Fl(i)p Fj(=1)11555 39223 y Fq(p)170 b Fp(\()133 b Fq(y)36 b(;)171 b(z)14241 39334 y Fl(t;i)15162 39223 y Fo(j)g Fq(\013)q(;)g(\016)-19 b(;)171 b(\033)36 b Fp(\))5774 42076 y Fo(\002)228 b Fq(p)7482 40972 y Fm(\020)8227 42076 y Fq(y)8731 42231 y Fj(1:)p Fl(M)72 b Fj(\()p Fl(\015)10967 42343 y Fg(t)11334 42231 y Fk(\000b)p Fl(\015)12788 42343 y Fg(t)13155 42231 y Fk(c)p Fj(\))13911 42076 y Fq(;)171 b(z)14885 41567 y Fj(1:)p Fl(M)72 b Fj(\()p Fl(\015)17121 41679 y Fg(t)17489 41567 y Fk(\000b)p Fl(\015)18943 41679 y Fg(t)19310 41567 y Fk(c)p Fj(\))14842 42341 y Fl(t;i)20066 40930 y Fm(\014)20066 41528 y(\014)20066 42126 y(\014)20578 42076 y Fq(\013)q(;)171 b(\016)-19 b(;)171 b(\033)23201 40972 y Fm(\021)23984 42076 y Fq(;)-1953 44807 y Fs(where)237 b Fq(z)1236 44298 y Fj(1:)p Fl(M)72 b Fj(\()p Fl(\015)3472 44410 y Fg(t)3839 44298 y Fk(\000b)p Fl(\015)5293 44410 y Fg(t)5660 44298 y Fk(c)p Fj(\))1193 45072 y Fl(t;i)6652 44807 y Fs(denotes)237 b(the)f(\002rst)f Fq(\015)13700 44918 y Fl(t)14249 44807 y Fo(\000)178 b(b)p Fq(\015)16207 44918 y Fl(t)16579 44807 y Fo(c)235 b Fs(v)-20 b(olatilities)236 b(of)g(the)g Fq(i)24561 44384 y Fd(th)-1953 45964 y Fs(replicate)250 b(at)g(iteration)f Fq(t)p Fs(.)-292 47129 y(Making)370 b(use)g(of)g(dif)-25 b(fuse)370 b(conjug)-5 b(ate)371 b(prior)f(distrib)-20 b(utions)20695 46706 y Fd(1)21452 47129 y Fs(for)370 b Fq(\022)399 b Fs(en-)-1953 48286 y(sures)321 b(that)h(the)g(prior)g(distrib)-20 b(utions)321 b(are)h(rapidly)g(\223for)-18 b(gotten\224,)341 b(leading)323 b(to)-1953 49443 y(a)254 b(maximum)g(lik)-10 b(elihood)254 b(estimate.)321 b(Our)253 b(sampling)h(strate)-15 b(gy)253 b(at)g(each)i(time)-1953 50600 y(is)315 b(to)g(sample)h(\()p Fq(\013)q(;)171 b(\016)38 b Fs(\))315 b(from)g(their)g(joint)h (conditional)g(distrib)-20 b(ution,)332 b(then)316 b(to)-1953 51756 y(sample)258 b Fq(\033)293 b Fs(from)256 b(a)i(Gibbs)f(sampling)g (k)-10 b(ernel)257 b(and)h(to)f(propose)g(block-based)-1953 52913 y(Metropolis-Hastings)j(mo)-15 b(v)g(es)261 b(for)g(the)g(e)-15 b(xisting)261 b(latent)h(v)-25 b(ariables)261 b(\(using)g(a)-1953 54070 y(Kalman-\002lter)348 b(and)f(forw)-10 b(ard)347 b(\002ltering)f(/)h(backw)-10 b(ard)348 b(sampling)f(proposal\))-1953 55227 y(before)250 b(proposing)f(ne)-25 b(w)250 b(v)-20 b(olatilities)249 b(using)g(the)g(same)h(proposal)f(strate)-15 b(gy)-65 b(.)-292 56392 y(Considering)310 b(a)i(sequence)g(of)f(250)g (observ)-25 b(ations)311 b(and)h(a)f(temperature)-1953 57548 y(scale)266 b(which)h(increases)f(in)g(a)g(piece)-25 b(wise)266 b(linear)h(manner)f(to)g(a)g(temperature)-1953 58705 y(of)317 b Fp(4)f Fs(in)h Fp(340)f Fs(steps,)333 b(using)317 b(250)g(particles)g(we)g(obtained)g(estimates)g(of)f(the) -1953 59862 y(three)252 b(parameters,)g(by)f(the)h(same)f(mechanism)h (as)f(that)g(used)h(in)f(the)g(to)-10 b(y)252 b(e)-15 b(x-)-1953 61019 y(ample,)230 b(of)223 b Fq(\016)322 b Fp(=)285 b(0)p Fq(:)p Fp(96)131 b Fo(\006)g Fp(0)p Fq(:)p Fp(02)p Fs(,)229 b Fq(\013)286 b Fp(=)f Fo(\000)p Fp(0)p Fq(:)p Fp(25)131 b Fo(\006)g Fp(0)p Fq(:)p Fp(01)224 b Fs(and)g Fq(\033)321 b Fp(=)285 b(0)p Fq(:)p Fp(31)131 b Fo(\006)g Fp(0)p Fq(:)p Fp(02)-1953 62176 y Fs(where)307 b(the)f(true)g(v)-25 b(alues)306 b(were)h Fq(\016)430 b Fp(=)392 b(0)p Fq(:)p Fp(95)p Fs(,)321 b Fq(\013)393 b Fp(=)g Fo(\000)p Fp(0)p Fq(:)p Fp(363)306 b Fs(and)g Fq(\033)429 b Fp(=)393 b(0)p Fq(:)p Fp(26)-1953 63332 y Fs(\(suggested)359 b(by)h([4])f(as)g(being)h Fn(consistent)f(with)g (empirical)h(estimates)f(for)-1953 64489 y(\002nancial)f(equity)g(r)-37 b(eturn)357 b(time)h(series)p Fs(\).)631 b(Figure)358 b(1)f(sho)-25 b(ws)357 b(the)g(estimated)-1953 65646 y(parameter)271 b(v)-25 b(alues)271 b(as)e(a)i(function)f(of)g(the)g (number)h(of)f(observ)-25 b(ations)270 b(incor)-20 b(-)-1953 66803 y(porated.)291 b(Figure)194 b(2)g(sho)-25 b(ws)193 b(the)h(v)-20 b(olatility)195 b(estimated)f(by)g(its)f(posterior)g (mean)-1953 67959 y(under)203 b(the)f(empirical)h(distrib)-20 b(ution)202 b(of)g(the)g(\002nal)h(particle)f(set)g(\226)g(as)g(the)h (distri-)-1953 69116 y(b)-20 b(ution)281 b(o)-15 b(v)g(er)280 b Fq(\022)309 b Fs(con)-40 b(v)-15 b(er)d(ges)281 b(to)f(a)g(point)g (mass)g(at)g(the)g(maximum)h(lik)-10 b(elihood)p -1953 70074 10835 45 v -746 70814 a Fd(1)-359 71127 y Fc(i.e.)271 b(uniform)207 b(o)-13 b(v)g(er)207 b(the)h Ft(\()p Fb(\000)p Ft(1)p Fa(;)157 b Ft(1\))208 b Fc(stability)h(domain)e(for)h Fa(\016)33 b Fc(,)211 b(standard)d(normal)f(for)-1953 72126 y Fa(\013)222 b Fc(and)f(square-root)g(in)-35 b(v)-13 b(erse)222 b(g)l(amma)f(with)h(parameters)g Fa(\013)262 b Ft(=)f(1)p Fc(,)222 b Fa(\014)307 b Ft(=)261 b(0)p Fa(:)p Ft(1)223 b Fc(for)e Fa(\033)32 b Fc(.)27024 0 y currentpoint currentpoint translate 0.32166 0.32166 scale neg exch neg exch translate 27024 0 a 27024 0 a gsave currentpoint currentpoint translate 270 neg rotate neg exch neg exch translate 27024 0 a @beginspecial 50 @llx 50 @lly 554 @urx 770 @ury 5040 @rwi @setspecial %%BeginDocument: mml_volatility2.eps %!PS-Adobe-2.0 %%Title: mml_volatility2.eps %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Thu Oct 20 16:41:37 2005 %%DocumentFonts: (atend) %%BoundingBox: 50 50 554 770 %%Orientation: Landscape %%Pages: (atend) %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 M 0 PFs V } for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 2 1 roll M PFs 0 V } for } if stroke grestore } def % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def end %%EndProlog %%Page: 1 1 gnudict begin gsave 50 50 translate 0.100 0.100 scale 90 rotate 0 -5040 translate 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 630 420 M 63 0 V 6269 0 R -63 0 V stroke 546 420 M [ [(Helvetica) 140.0 0.0 true true 0 (-11)] ] -46.7 MRshow 1.000 UL LTb 630 1120 M 63 0 V 6269 0 R -63 0 V stroke 546 1120 M [ [(Helvetica) 140.0 0.0 true true 0 (-10)] ] -46.7 MRshow 1.000 UL LTb 630 1820 M 63 0 V 6269 0 R -63 0 V stroke 546 1820 M [ [(Helvetica) 140.0 0.0 true true 0 (-9)] ] -46.7 MRshow 1.000 UL LTb 630 2520 M 63 0 V 6269 0 R -63 0 V stroke 546 2520 M [ [(Helvetica) 140.0 0.0 true true 0 (-8)] ] -46.7 MRshow 1.000 UL LTb 630 3220 M 63 0 V 6269 0 R -63 0 V stroke 546 3220 M [ [(Helvetica) 140.0 0.0 true true 0 (-7)] ] -46.7 MRshow 1.000 UL LTb 630 3920 M 63 0 V 6269 0 R -63 0 V stroke 546 3920 M [ [(Helvetica) 140.0 0.0 true true 0 (-6)] ] -46.7 MRshow 1.000 UL LTb 630 4620 M 63 0 V 6269 0 R -63 0 V stroke 546 4620 M [ [(Helvetica) 140.0 0.0 true true 0 (-5)] ] -46.7 MRshow 1.000 UL LTb 630 420 M 0 63 V 0 4137 R 0 -63 V stroke 630 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MCshow 1.000 UL LTb 1896 420 M 0 63 V 0 4137 R 0 -63 V stroke 1896 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 50)] ] -46.7 MCshow 1.000 UL LTb 3163 420 M 0 63 V 0 4137 R 0 -63 V stroke 3163 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 100)] ] -46.7 MCshow 1.000 UL LTb 4429 420 M 0 63 V 0 4137 R 0 -63 V stroke 4429 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 150)] ] -46.7 MCshow 1.000 UL LTb 5696 420 M 0 63 V 0 4137 R 0 -63 V stroke 5696 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 200)] ] -46.7 MCshow 1.000 UL LTb 6962 420 M 0 63 V 0 4137 R 0 -63 V stroke 6962 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 250)] ] -46.7 MCshow 1.000 UL LTb 1.000 UL LTb 630 420 M 6332 0 V 0 4200 V -6332 0 V 630 420 L LTb 140 2520 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true true 0 (log Volatillity)] ] -46.7 MCshow grestore LTb 3796 70 M [ [(Helvetica) 140.0 0.0 true true 0 (Time / steps)] ] -46.7 MCshow LTb 3796 4830 M [ [(Helvetica) 140.0 0.0 true true 0 (Reconstructed Volatility)] ] -46.7 MCshow 1.000 UP 1.000 UL LT0 LTb 6311 4487 M [ [(Helvetica) 140.0 0.0 true true 0 (True Volatility)] ] -46.7 MRshow LT0 6395 4487 M 399 0 V 630 3263 M 25 51 V 26 -54 V 25 -170 V 25 93 V 26 -24 V 25 200 V 25 -207 V 26 -170 V 25 148 V 25 -73 V 26 162 V 25 -25 V 25 136 V 26 -83 V 25 77 V 25 -155 V 26 -171 V 25 -56 V 25 -400 V 26 -458 V 25 -217 V 25 -82 V 26 108 V 25 50 V 25 353 V 26 21 V 25 -243 V 25 -32 V 26 -7 V 25 -192 V 25 89 V 25 173 V 26 61 V 25 -95 V 25 -58 V 26 -377 V 25 206 V 25 -11 V 26 17 V 25 -85 V 25 107 V 26 -35 V 25 80 V 25 -43 V 26 216 V 25 -193 V 25 -264 V 26 108 V 25 -215 V 25 132 V 26 142 V 25 -79 V 25 57 V 26 327 V 25 -324 V 25 0 V 26 -130 V 25 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26 -77 V 25 -86 V 25 -132 V 26 -138 V 25 -56 V 25 -2 V 26 -132 V 25 -182 V 25 -172 V 26 -88 V 25 -67 V 25 -220 V 26 -166 V 25 -92 V 25 -52 V 26 48 V 25 96 V 25 -46 V 26 -173 V 25 -131 V 25 -52 V 25 -88 V 26 -4 V 25 -31 V 25 -81 V 26 33 V 25 95 V 25 89 V 26 -28 V 25 -96 V 25 -117 V 26 -98 V 25 -38 V 25 36 V 26 -32 V 25 -6 V 25 38 V 26 114 V 25 130 V 25 52 V 26 104 V 25 189 V 25 48 V 26 127 V 25 95 V 25 1 V 26 -32 V 25 8 V 25 118 V 26 -24 V 25 97 V 25 10 V 26 64 V 25 30 V 25 121 V 26 -36 V 25 -1 V 25 -73 V 26 74 V 25 72 V 25 112 V 26 151 V 25 209 V 25 171 V 26 59 V 25 98 V 25 128 V 26 192 V 25 233 V 25 90 V 26 80 V 25 21 V 25 21 V 26 1 V 25 26 V 25 39 V 26 98 V 25 -89 V 25 -124 V 26 -114 V 25 -69 V 25 -59 V 26 45 V 25 30 V 25 -145 V 25 -105 V 26 -96 V 25 12 V 25 30 V 26 7 V 25 57 V 25 100 V stroke 3213 3198 M 26 51 V 25 47 V 25 -108 V 26 -189 V 25 -154 V 25 -59 V 26 88 V 25 0 V 25 115 V 26 96 V 25 149 V 25 150 V 26 163 V 25 120 V 25 -96 V 26 -69 V 25 3 V 25 16 V 26 51 V 25 -97 V 25 -52 V 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