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1.5

1.5

PLE MnE

0.0

0.0

0.5

0.5

1.0

1.0

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PLE MnE

−1.0

−0.8

−0.6

−0.4

−0.2

0.0

0.0

0.2

0.4

0.6

0.8

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0.6

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2.5

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PLE MnE

1.5

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0.0

0.0

0.5

0.5

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1.0

Density

1.5

PLE MnE

−1.0

−0.8

−0.6

−0.4

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0.010 0.005 0.0 -0.005 -0.010 -0.020

-0.015

bias of the estimate

MLE(X) MnE_3 MnE_4 MnE_5 MnE_6 MnE_7 MnE_10

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

phi

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0.16 0.14 0.12 0.10

Standard Error of the estimate

MLE(X) MnE_3 MnE_4 MnE_5 MnE_6 MnE_7 MnE_10

-0.6

-0.4

-0.2

0.0 phi

â ·ÉE¿jº»¸U³j¾@³Íµ¤¹ç¼È¥°kº<·g¸d¹E¹ ¹E½I¸‰¼&°P¹*ºÍ°kº<º¸™º»º ¾jk° º
o ¯

0.2

0.4

0.6

¹%º§¹˜½GË~¹ÍÎ Ò·¼»·æË~åiΪÂbç Ä )½ ¹%º

0.030 0.025 0.020 0.010

0.015

MSE of the estimate

MLE(X) MnE_3 MnE_4 MnE_5 MnE_6 MnE_7 MnE_10

-0.6

-0.4

-0.2

0.0 phi

0.2

0.4

0.6

â ·ÉE¿jº»¸U³j¾–ïǵ¤¹ç¼È¥°kº<·g¸d¹E¹§¹E½iË Ì“Î E¹ ½iË~¹ÍÎ Ò·¼»·œË~åiΪÂbç Ä ½)¹%º‡¾j°kº<·g¹E¿¥¸«¾Ž°P²  ¿ ¸dJ¸ ¹˜½ K °P¹¥º φ

o§

0.9 0.8 0.7 0.6

Efficiency of the estimate, comparing to MLE(X)

MnE_3 MnE_4 MnE_5 MnE_6 MnE_7 MnE_10

-0.6

-0.4

-0.2

0.0 phi

0.2

0.4

0.6

â ·ÉE¿jº»¸U³j¾–ðǵ¤¹ç¼È¥°kº<·g¸d¹E¹¨¹˜½ ¦¸d²°j¼À·¾$¸ÒÎØÁ ·¸d¹*Á ·¸d¸Â¹˜½¤Ë~¹ÍÎG·¼»·‹Ë~åhΪÂ_ç Ä )½ ¹%ºÒ¾jk° º
o

0.10



0.06 0.04 0.0

0.02

Actual Type I Error

0.08



20x20 Field 30x30 Field 40x40 Field

 â ·ÉE¿jº»¸U³j¾¢ôµ 2 °ŽÈ¥È0º»¹Í· ¼Ã°j¼À·¹¹Ñ½)¹%º^¼»·j¸ÃÁ³º<·¼ ·gÁ °P²›¾j°P²c¿j¸d¸¦¹˜½ ê å ã¶(½ ¹çº^¼Ì¸d¸‰¼ ÷¹˜½Ð·g¹¥ºj¸¬È¸d¹¥ºj¸d¹¥³Á ¸ 0.0

0.02

0.04

0.06

0.08

0.10

Theoretical Type I Error



 6 (+89!:/!:(+89!;(+<=! "!$#%'&)(+*-, .0/21%'3+!$#'&4#51 7

± ± ‹ Š Š ‹ Ñ¥Œd™ ßkšŠš™ŽŒ ²³šbŠ6—˜ ŠšŒHŒdšbŠŽ:¥˜kφ­ˆŠšŒ0š_Š6²ݐ™ ßç‹ ²CŠ™ŽŒdšT—š—˜Š™Ž‹ Œ¤‹™kŠ ² ²³­ Œ˜ŽŒd²³£Ôš]µ ‹ š_Œ”—š+Šš™jŒ¤™ í ß$²CŠ™ŽŒdšT—š²Ý°¥˜k± ´ŽŒߐŒ˜k´ŽŒd˜Ôµ†Œ 8 ’ê+˜ŽŒzµ ˜Œ£kšŒ¦Šš™jŒiß .  Œ‰Šˆˆ—µ¤‹ —ç²"²CŠŽšbŠŽ ßJßԍˆ²"µ†Œd´Ô£kŒ ŠŽ²ªŠšŒdbš Š¦Šš™k¥qš ™ ßçC² Š™ŽŒdšT—†š ’i.  ŒdŒx’Œ¤µ²³˜kšT—´ŽŒqŠš™ŽŒã£kš_ŒÂ²àÝ–¥ Œ–—–™k²Ö²"´Öí) Šˆ—²ãßkˆ²"µ†Œ´k£k_Œdš†’ ¢Š .²³‡Šš™ŽŒšbŠ ‹ ˜k´ ‹ ˆ´¨–¥ Œ–—–™k²Ö²"´§ ‹ Šˆ—‹²UŠŒdšbŠŽšd¯²³˜ŽŒµ ‹ ˜Ø‹ — ‹ š_Œ‘ô Šš™ŽŒ‘ŠŒdšbŠ:ßkˆ²"µ†Œ´k£kŒ ²˜ÚŠš™ŽŒ  –— – Šˆ—˜k­ ÷ ‹ ´k¥_š ‹ Šˆˆ —ÔŠ j£ ŠŽ¥²³Ç˜ ’#z²»’ ŒCå Œd¯ š+˜kC² ŠÞ Œd´“—˜“›ú ™ jß ŠŒdŠ ¯“Š™ŽŒ{ßkš_Œd£k´Ô²àí׋ ” Ћ Ù ‹ Ñh” ÐÙ ´k§²Š Œšä˜kC² Š›™ å Œ –— N ŠŽ¥˜k­ ÷ Š ´k—bš ŠŽ‹ T —kj£ Šˆ—²³“˜ ’ ‘˜ Š™k—šßk‹ ˆ ² —ԏ– Œ ‹ ¬¯ Šš™ŽŒxhÑ ” ÐÑÙ ™ ‹ š šˆµ – Œd‹´ ÷ –— –Šˆ—‹ ˜k­z´k¥š_ŠŽT—k£§ŠŽ—²˜Ç’0êx£Ôšˆ £k– Šˆ—²³˜ÔšŒšˆ£k–N‹ ŠÝ²³]å ˆ¥²³‹ £kšµ ‹ šŒššT£k­³­ ŠŒŒš_‹ ŠhŠš™ ŠŠš™ŽŒ”. šˆµ –—¥˜k­ µd²³˜kbš Š ˜ Š:¥š{ә£k– ŠŒ¦µd–¥‹ ²³š ŒÒŠˆ²“²³Ž˜ Œà¯šT!² Šš™ŽŒ£Ôšˆ£ –Ò`µ ™k‘í)šˆÓ™£ _ Œd´ ßkßԍˆ²áÖ ŠŽ¥²³˜§’²³ š:ә£kN ŠšŒ ›’ Œ–—–°Þ ݲ³q Š™ŽŒÂiÑ ” Ðõ Ù –¥šˆŽ² ’ ± ŠŒ‹ ‹ ŠŒ‹ ‹ > ˜  ¢ —  ³ ­ Ô £ ŒxûŽ’ ¯.’›Œ¤š_Šˆ£kÞ ´ Šš™ŽŒÂßEŒdTݲ ˜kµ†Œã²Ý*Šš™ŽŒ ± ßkßÔލˆ²áÖ ŠšŒ‡ ” ÐÙ — šŒ´8²³˜“þr˜.ÿ  ‹ ‹ Š™ŽŒdh ŠšŠ2™ ‹ ‹ G˜ Šš™jŒ® hÑ ‹ ” Ð#Ù ’ G˜ Šš™Ô‹ —š‹ â.­³£k_ Œ¬¯ Šš™Ž‹Œz˜k² Š‹ —˜ ‹ ‹ j– Š ß Œ ŒdTˆ²³Tš — ‹ _š Œd´¦²³˜J‹ `µ ™kîí šˆÓ™£ ‹  Œd´ ßkßkT²ÌÖ Šˆ—²³˜  Œ+ßk–¥C² ŠŠŒd´ ­ —˜Ô_š ŠiŠš™ŽŒ ‰µ ŠŽ£ –$å –¥Ž£ ŒdšÝ²³ Š™k Œ‰Œx´k– ϐŒd_ Œd ˜ Šæ– ŠŠˆ—†µ Œ†š ’]¤Ù ™Ô—š oô 0

2

2

2 1

0.05 0.0 -0.05

20x20 30x30 Field 40x40 Field

-0.10



-0.15

Relative Error of Approximation



 â ·ÉE¿jº»¸Y³ ¾–öǵ?>Á ²¹E¸d¸™ºÒ²¹°¹[email protected]‹°j¼ª¼»· ¸

0.0

0.02

0.04

0.06

0.08

Theoretical Type I Error

÷

2

0.10

°ŽÈ*Èjº»¹BÍ·g¼°j¼ ·g¹E¹

.

‹ ‹ ‹ Œ Š ‹ â.‹{­³Š £k_Œäš™k²Ì’”‹ š+Šš™ Š%Š™Ž. Œäµ`™k± ‘í)šˆÓ™£ _Œd´ ßÔßkˆ²áÖ ‹ ŠŽ¥²³˜x’Ò² š6ýÓ"£Ô–ŠšŒ’›Œ–—–g’‹ ¢¥­³£k_ŒÒûŽ’ ßkT²»å"ŠŒ¥´Ž‹ Œdš ²³_Œi´jŒ‰Š Ꮧ–Œ´2–¥± ²Ö² — µd²³˜Ô šˆ—´jŒdˆ¥Þ˜k­Š™ŽŒ®_‹ Œd– ŠŽ‘å ‹ Œ ŒdˆT²³Š †’ Œ®š_Œ†Œˆ‹ Š™ Š›Š‹ ™k—š—šә£kŠŒ–Š‹ Œ®š –¥– ŒFÖµ†ŒßjŠ¤Ý² å Œ µ–—²³_š Œ0ŠŽ² ŒˆŽ² ’ Šã—š+µ– Œ ˆ Šš™ Š®Ýˆ² Šš™k¥šˆŠš™ ŠˆŠš™ŽŒ ßkßkˆ²áÖ Šˆ—²³˜H—š Œ ‹ šˆý ²³˜ ‹ —k– Œž’  Š ‹ Š ‹ ± Œä˜k²Ì’ Š Šˆ£kˆ‹ ˜0Šˆ²Âßç²Ì’›Œµd² ß T—šT²³˜kš†’0¢¥­³‹ £kŒÒûŽ’ š_™k²Ì’”šŠš™ŽŒ”Œšˆ£k–NŠŽš²ݘŠ™ŽŒäšˆ £k‹ – ŠŽ—²‹ ˜ _š ŠŽ£Ô´  ŠŽ²rµd² ß _ ŒªŠ™ŽŒJß$²Ì’ ŒdÂ£ ² ›Ý Š™ŽŒIŠŒdbš Š•— ± š Œd´•²³œ ˜ Š™ŽŒGH”jÐ0Ù φ²Ýzþr0˜.ÿ’”– Š™œŠ™ŽŒ ‰µ ŠŽ£ – ‹ ‹ ‹ ‹ ”jÐ0Ù — _š Œd´“²³˜>– ŠŒd ˜ Š®´ Š ’ç¤Ù ™ŽŒ{˜™£k–¥Í– ™ ßçC² Šš™jŒdšˆ¥š+—š 8 8 ’i¤Ù ™ŽŒ¤â.­³£k_ Œvš ™Ô²»’”š ‹ ‹ ‹ ‹ ‹ φ 0 φ K ™k²Ì’ኚ™ŽŒãßç²Ì’›Œzå TŒdšä’”NŠš™ ݲ³äå ˆ¥²³£kšæå –—£jŒdšä²Ý ’Ù¤™ŽŒãå –—£ŽŒ Š 8 µd²³TŒšˆßç²³˜k´kš ŠŽª ² Šš™ŽŒÂ– ŒF å Œdg– ’æÕ"—˜k‰µ Œ‡Š™ŽŒã– ŒCå Œd–¥š ‹  Œ ‹ –—– ± ‹ ŠŒ—$Š ²³§£ Š¤Šš± ™ŽŒÂš ‹Š Œ¯.N Š”—š Š Œ ‹ ˜k¥˜k­Ý£k‹ – ŠŽ²Jµd² Š  ß ‹ _ ŒˆŠš™ŽŒ ´k– ϐŒd_ Œd ˜ Švß犌²Ì›’ ‹ Œvµ£kTCå ‹ Œd†š ’YÛiC² ŠŒIŠ™ŽŒJš Œ‰Šˆ ²‹ ›Ý Šš™ŽŒJß$²Ì’ ŒdÂÝ£k˜k‰µ Šˆ—²³˜ ‹ ˆ²£k˜k´ ŒdKTŽ² ’ì«®š —˜ÚŠš™jŒÓŒdš_Šˆ ŠŽ¥²³˜•ŠŒµ ‹ šŒà¯Šš™ŽŒßç²Ì’›Œé²Š Ý®þH‹ ˜.‹ ÿí]— šŒd´ëßkT²Öµ‰Œd´k£k_‹ Œdšé¥˜kµd_Œ š_Œdš{’”‹ –Š™ ‹’¬‹ ¢.²³ K 8 10 j¯ Šš™jŒÂEß Œd^ݲ³ ˜k‰µ Œ+—šäә£kN ŠšŒãµd² ß  —k–– ŒÐŠˆª ² Š™ŽŒ‡” ÐòÙ — š Œ´>²³Ó˜ Šš™jŒÂ– ŠšŒ ˜ Šä´ Š ’

o

0

û

1.0 0.8 0.6 0.4 0.0

0.2

Power of the test (phi==0)

MLE(X) MnE_3 MnE_4 MnE_5 MnE_6 MnE_7 MnE_10

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

phi



ý

â ·ÉE¿jº»¸Y³ ¾ǵ ê ¹Bv¸™ºG½)¹%ºI¼»·j¸¼Ì¸d¸‰¼J¹˜½«·c¹*º ¸¬È¸d¹*º ¸d¹*Á³¸ DCE1GFIHKJLM/9N4!O1QPRH0&LM/9N4!OST!$*QPU!$#V#V&1Q( WXPU1QY9N4!:L

±

ý  Š ‹ ‹ ‹ ŒH˜Ô²»’ š_ŠŽ£Ô´ Šš™ŽŒr˜k²³˜Öí ™k² ²³­ Œ˜ŽŒd²³£Ôšéµ š_ŒC’ ŒHµ²³˜kšˆ¥´ŽŒd  šˆ—˜Ô­³–Œ– ŠŠˆ—µ†Œ²àÝ+šˆ Œ ‹ šˆšˆ£ Š Œ‡Šš™ ‹ Š¦Š™ŽŒv––ŒÝŠ ™ ‹ –‘Ý]²Ý*Šš™ŽŒ¤– ‹ Š_ŠŽ—µ‰Œ#™ ‹ š Š Œ ‹ ˜ ŒdT² ‹ ˜k´Šš™ŽŒ¤ˆ¥­ ™ ŠÐ™ ‹ –¥Ý 20 ‰ 20 ‹ k ˜ ´ ‹™ š Š Œ ‹ ˜ β ’ ý Œ®µd²³˜kšT—´ŽŒ›Œ_š ŠŽ Š2‹ ŠŽ—²˜Œ²Ý β ‹ šÒ›’ Œ–—– ‹ š φ ‹ ˜k´ÒŠ™ŽŒ+µ£jŠTí)ß$²³¥˜ ŠŽš Θ ’]Ù¤™k—šµ ‹ ˜ . ‹ ‹ ‹ ‹ Š ‹ ‹ ‹ ‹ ‹ —ŒÂå֏–Œ’Œd´ š šTÞ ßŒµd –0µ š Œ¤²Ý6 Œ­³ Œšˆšˆ¥²³˜>ßԍˆ ² —k–– Œ šz’”N Šš™ šˆ¥˜k­³–– Œ¤µ²»å T ŠŒ#± Šš™ Š Š Œdš ²³˜„Š ’Ò‹ ²å ‹ –—£jŒdš†’ ‹ŠãŠ µ ‹ ˜ ‹ –¥šˆ²Ó—EŒvŠ å"ŒF’›Œ´ ‹ ‹ š ‹ Š ’²àí š ‹Š ßk–Œ¤ßkˆ‹ ² —Ô–Œ Š ’ÂÙ¤™ŽŒé ²³˜k10– ‰ ´k20NϓŒŒ˜kµ†Œ —šˆŠš™ Šá¯ —˜!‹ Š ’²à‹ í)š ßk– Œv‹ ßkˆ ² —ԏ– Œ šd‹ ¯°’ Œª20™ å‰ Œª20Š ’Ò²r´kN ϓŒŠŒ Œd‹ ˜ . Šã– ‹ŠŠˆ—†µ Œš+²Ýšˆ Œ ±¦’ ™k—–– Œ ‹ ™ŽŒd_ Œv›’ Œ•™ å Œ šˆ—˜Ô­³– Œã– ŠŠŽ¥†µ Œ#Šš™ Š®¥š ’”¤Ù ™k—š Œš ´kN ϓŒ Œ˜k†µ Œ¤—^ ˜ Šš‹ ™ŽŒÂ’ Šš™Ž‹Œ ‹ ‹ ‹ Œd´k­ ŒÂšˆNŠšŒš Œ#ŠŽ_Œ ŠŒd´r—˜^Šš™ŽŒ#Š ’²2µ šŒdš‰’qÛ Œå Œ_Š™ŽŒd––Œdšˆš¯EŠ™ŽŒÂŒdšT£k––Šˆš”ßkˆ²Ìå"—´ŽŒ ­³²"²Ö´¥´ŽŒ ²*Ý Š™ŽŒãß ŒTݲ³ Š2‹ ˜k†µ Œx¥‘˜ Š ’Ò²àí)š ‹Š ßk–– Œxßkˆ ² —ԏ– Œ Š †š ’ Î#¸‰¼À·g ¼ °j¼À·E¹ ¹ ± ý φ‹ ⠌ Š ‹ ‹ Œ6µd²³˜kšT—´ŽŒ°â.ˆšbŠÍŠš™ŽŒ6ßkT²³ßŒ_ŠˆŒdš„²àݧŠ™ŽŒhŒdš_Šˆ ŠŽ² ˆ š°²Ý ˜Ô´ ’ê+˜k– Šš™ŽŒhŒÓ"£Ô—ßkT² — —k––Œ µ ‹ _š ŒŒ’”– Š™ K 8 3 —šãbš ŠŽ£k´k– ŒdÇ´ ’2¢—­£k ŒšÂjû ’ ¯ ‹ ˜Ô´•Žû ’ š ™k²Ìz ’ Š™ŽŒª—k ‹ _š ŒdšÂ²›Ý Š™ŽŒIŒd_š Šˆ ŠŒ‹ ŠŽ² o o

0.0 -0.010 -0.015

bias

-0.005



0 0.4 0.8 1.5 2

0.0

0.2

0.4

0.6

phi

â ·cÉE¿ º  ¸ ³ ¾c´ZÕµ¦¶·°P¸{¹˜½«Ë~¹ÍÎ0±*°P¸¸§º¸d¸‰¼À·g¼°j¼á¹çº:¹˜½

φ

½)¹%ºG¾j°kº<·g¹E¿¥¸¾j°P²c¿j¸d¸é¹˜½

β

± ‹ ²‹Ý £kšT—˜k­þH˜.ÿ ˜k´§þY£ ”  ÿ ŒdšTߐŒµ‰Šˆ¥å Œ‹ – ’xÙ¤™ŽŠ2Œd‹ _Œé—š Š ‹ šˆ–—‹ ¥­ ™ Š®£Ô˜k´ŽŒd‹ _ŒdšbŠŽ‹  ŠŒ‹ Šˆ—²³˜r²Ý φ ¥˜ ‹ –¥– µ š_Œdšz—˜kµ–—£k´k¥˜kÀ ­:þY” ÿ ’%ØÒ£§‹Š Š™Ž‹ Œ#—k šä‹ —šäš‹ –¥–Úµ² ß Œ´^Šˆ²:š_Š Š2˜k‹ ´ T´Œ⍈T²³ˆš‰’ ý ¢¥‹ ­³£k_ŒvûŽ’ ‹ š ™Ô²»’”Ÿš Šš™jŒ—k š ˜k´ù_š Š ˜k´ ‹ T´­ŒdˆT²³®Ý²³ˆ‹ Š™ŽŒÞ ŒdšbŠŽ ‹ ŠŒv²Ý £kšˆ¥˜k­HþH˜.ÿ¤‹ ’ ŒŒµ ˜¬šŒ†ŒªŠš™ ŠŠ™ŽŒd_ŒŒ¥šã˜k²>µ²³˜kšˆ¥š_ŠŒd˜ Š•—ԏ šã—˜­Šš™Ô—šãµ š_ŒC’ ˜§Ý µ‰Šd¯0NŠã—šãß$²šˆšˆ–—k–ŒŠ™ Š ‹ Š2‹ ⠘ Š™k—qš Š ’²àí š ‹Š ßk– ŒxßkT ² —k–– Œ Š —EŒdµ ‹ £k_š Œ‡Š™ŽŒŸ—k ‹ š_Œdš Šš™ŽŒvþH˜.ÿ¥š”£k¬˜ —k _š Œd´ìݲ³¤ Œdbš ŠŽ Šˆ—˜k­ ˆ —Ó µ ‹ ˜k‰µ Œd– ²³j£ Š†’¤Ù ̙Žô Œã_š Š ‹ ˜k´ ‹ T^´ ŒdˆT‹ ²³ˆšäݲ³ ⠏—˜Ôµd Œ ‹ š Œx’”N Šš™ φ ’ Š2‹ ⠊ ‹ ¢ ¥­³£k_Œ®ûŽ‹ ’ ‹ š_™k²Ì ’”MLE š¦Š™ŽŒxXŒ– Šˆ¥åCŒˆ‹ ŒèJµd–Œd˜kµ‹ Œšæ²Ý͊š™ŽβŒÂþr‹ ˜.‹ÿ Œš_ŠŽ ŠŽ²³²φÝ µ² ß Œ‹ ´‘ŠŽ² ž Ÿ ݲ³iå T—²³£kšzå –—Ž£ Œš®²Ý š Ý£k˜k‰µ Šˆ—²³˜>²Ý ’x¤Ù ™ŽŒš Œéå –—j£ Œdš Šš™ŽŒ £k˜k ² —jŠ —˜ —k– Œ φ Š ‹ β ‹ ‹ ‹ 5 À 10% š Œ†Œ ¥š ŠŽ ² —Œµd²˜k_š Š ˜ Š¥˜ ’j¤Ù ™ŽŒiŒèJµd– Œd˜kµ Œdš0Ž´ Œdµ Œ š Œ’”– Šš™ ’”– Š™ –—²³šTš ²Ý —ç²³j£ Š ݲ³ φ 8 Ï 5 ’ [ äÕÈP¹ ¼»· d¸ ¸&·g¸:¶Òd¸ ¸‰¼ ·g¹ÍÉ ± . ý ‹ ‹ Œ Š ‹ ‹ Œ¦˜k²Ì’ µd²³˜kšT—´ŽŒ0™ ß$²CŠ™ŽŒdšT—š0ŠŒdš_Šˆš— š_Œd´ ²³˜ ßkßÔ± ˆ²áÖ ŠšŒJ–— Œd–¥™k²"²"´¬ ŠŽ¥²>ßkT²Öµ‰ŒFí ´k‹ £k Œ†šH’2¢%: ²ˆβ Šš™k¥0šÂ_ Œd­³_ ŒdšTšˆ—²˜¬ßk± T ² —k–– Œ Š “¯ Šš™ŽŒ ‹ Œ ‹  ŒŠ ’U² ™ Š ßçC² Šš™ŽŒš Œ± šv²Ýҏ—Š ˜ ŠšŒ‹  Œdbš Š H : φ 8 0 8 ¤Ù ™ŽŒ:â.T_š Š0™ ßçC² Šš™ŽŒšˆ¥š¤¥š ŠšŒ_š Š{²àqÝ ™k² ²³ ­ ŒŽ˜ ŒdN Š ²Ý Œ ˜kšÂ—­ ˜k´ ˜ Šš™ŽŒJßk Œš^í φ

0

0

o

k

-0.005 -0.020

-0.015

bias

-0.010



0 0.4 0.8 1.5 2

0.0

0.2

0.4 phi

â ·ÉE¿jº»¸Y³ ¾c´˜´Pµ¤¶·c°Ž¸:¹˜½ Ë~åiÎÂ_ç Ä E¹ ½

‹ ‹

φ

0.6

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Index of the Sampler

0

5000

10000

15000

20000

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−0.3

−1.0

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Index of the Sampler

0

5000

10000

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0.1

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Index of the Sampler

0

5000

10000

15000

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Index of the Sampler

5000

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15000 Index of the Sampler

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Modeling and Inference for Spatial Processes with ...

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