Introduction to MCMC * Petros Dellaportas and Gareth O. Roberts ...

Ï+ ¬…6/)rq?â + Ý€®ž­3¥qª¤¥ž­Ê°a¨V«Ê­M¥q­f¦:q]Ý€­f®ž² ¥Z§f¥q²0ā±Ÿ¢g).¢ t v7y7y@yª¢š¸ + Ý€­f®ž² ‚ º ¥qªy¹_¥qª¢_§T«Ê¨Ÿ²¥.«f¢Ž6/)qÄñ+Æbbo°»‚ø¥Ä{Åt‚ º ñÄ+ÆÆÆb¹ ( „tˆ>¦=tˆ‡3ˆV (Ç …G¥Z‡ „†… ¦‰ …º ( ƒ ( ƒ Š μy§Ê¨Vªa¬Z«Ê¡a¢,¢_§T«Ê¨Ÿ²0¥q«Ê®­‚ º )£¢v )RÅq´ +)£¢Ð]¡a¨Ÿ¹M¡ ¨©§¥žªï¼aª{°a¨Ÿ¥§T¢!ÿ¢_§T«Ê¨Ÿ²0¥q«Ê®­=®qÝ 6/)q + ¬…6/)rq?â +k ­f®ž²ë«Ê¡a¨©§§Ê¨Ÿ²Â¼a±©¥.«f¨V®ª «f¡a¢-­f¢Ý€®­Ê¢¥-†Ð,¢6¹_¥qª ¢_§T«Ê¨Ÿ²¥.«f¢¢ + ¬A|)rq?â} ¢ + Ý€­Ê®²Åž´œ-y¥žªy¨V²0ā­f®.Ꞣ³®¼a­Ä¢!§k«f¨V²¥.«f¢®qÝ3«Ê¡y¢ÂØ+!¨ÆÄ+ †¡a¨©§Zȳ­Ê®·¹¢!·¼a­f¢³¨Ÿ§Ä¼y§T¼+¥q±Ÿ±V¦C¨¸«f¢-­M¥.«Ê¢!|g)rqš}¥¤ª{¼a²¤°+¢_­]®qݦ«Ê¨Ÿ²0¢_§†¼aª¢«Ê¨Ÿ±º«f¡a¢³¢_§T«Ê¨Ÿ²¥.«Ê¢!C«Ê¢-­f²§]§k«M¥q°a¨Ÿ±Ÿ¨Ÿ§Ê¢žË Ž ç®´8”©²A“È‘wŒ$²AGš‘w²A”–Ž Zµ¨©§¥§k«f®{¹M¡+¥ž§T«Ê¨©¹c¥ž±V¬®ž­f¨¸«f¡a² Ý€®­²0¥qÇ·¨V²0¨©§T¨Ÿªa¬ìÝ€¼aªy¹«Ê¨Ÿ®žªy§_û)«¤¨Ÿ§¤êž¢-­f¦é¹±Ÿ®§Ê¢-±Ÿ¦é­f¢-±©¥.«f¢_¿yµ Ø µ + †¡a¢®žªa±Ÿ¦Ca¨Ê.$¢-­f¢-ªy¹-¢¨Ÿ§]«Ê¡y¥q«]«Ê¡a¢«M¥q­f¬ž¢-«]a¢-ªy§Ê¨¸«k¦ì¹M¡y¥qªy¬ž¢_§]¥§Ñ«Ê¡a¢¤¥q±Ÿ¬ž®ž­f¨V«Ê¡a² ȳ­Ê®·¹¢_¢_a§_ k ¨V­M§T««Ê®=تa®q«f¨Ÿ¹-¢C«f¡y¥.«C¨¸Ý³Ð,¢ÙІ¥qª¢«0«Ê®Ó²¥qÇ{¨Ÿ²0¨Ÿ§Ê¢é¥ ªa®žªb¨'ªa¢_¬¥q«Ê¨Ÿêž¢ìÝ€¼aªy¹«Ê¨Ÿ®žªCX)+ v|·Á-Ñ«Ê¡a¢é²¥qÇ{¨Ÿ²0¨Ÿ§Ê¨Ÿªa¬;ê@¥ž±V¼y¢¥q±©§T®Ó²¥.Ç·¨Ÿ²0¨Ÿ§Ê¢_§X)Ý€®ž­C¥ž­Ê°y¨¸«f­f¥ž­Ê¦ìŸ £ ¤ÓÒ{ªa®.Ð]ªÍ¥ž§=«Ê¡a¢6«Ê¢_²c¯/¢-­M¥.«f¼a­f¢ž ÛÄ®.Ð,¢_Ꞣ-­=Ý€®ž­±©¥q­f¬ž¢ÇŸÁ-+ t ©¥ž§f§T¼a²0¨Ÿªa¬¤«f¡y¥.«Jt ©+ t ©¨Ÿ§†¥qª¨Vª¢«Ê¢_¬ž­M¥q°a±Ÿ¢ZÝ€¼yªy¹X«f¨V®ª§-{«Ê¡a¢³·¨©§k«f­Ê¨Ÿ°a¼·«f¨V®ªÐ]¨V«Ê¡·¢-ª+§T¨V«k¦ā­f®ž¯/®ž­Ê«Ê¨Ÿ®žªy¥ž±a«Ê®…£)¹®žª+¹¢-ª¢«f­f¥q«Ê¢_§¤²c®¢§k«0®qÝZ¨V«f§cā­f®ž°+¥q°a¨Ÿ±V¨V«k¦ ²0¥§Ê§¤¨ŸªÓ«Ê¡a¢ìê{¨Ÿ¹-¨Vªy¨¸«k¦;®qÝÄ«Ê¡a¢C²c®··¢ì®qÝ]«f¡a¢CÝ€¼aªy¹X«f¨V®ªºÓ †¡a¢¨©·¢!¥°+¢_¡a¨Vª+é§T¨Ÿ²Â¼y±Ÿ¥q«Ê¢_6¥qªaªa¢!¥q±Ÿ¨Vªy¬=¨Ÿ§@-$¥.«¢!¥ž¹M¡Ù¨V«Ê¢_­f¥q«Ê¨Ÿ®žªÙª§-/«Ê®C¹-¥q­f­f¦®ž¼a«tØ µ Ø µ ®ª6¥=·¢_ªy§Ê¨¸«k¦ā­f®ž¯/®ž­Ê«Ê¨Ÿ®žªy¥ž±«Ê®yšt ©¹-®žª{Ꞣ_­Ê¬¢_§¼ -aÐ]¡a¢_­Ê¢mŸ ¸ ¨©§Z¥§Ê¢@2¢¼a¢_ªy¹¢³®qݦ«Ê¢_²0¯+¢_­f¥q«Ê¼a­f¢_§†«f¡y¥.«Ä¹-®žª{Ꞣ_­Ê¬¢_§,«Ê®…†_¢-­f®yI †¡a¢¤¥ž±V¬®ž­f¨¸«f¡a²«Ê®«f¡a¢¤²¥.Ç·¨Ÿ²Â¼a²äê.¥q±Ÿ¼a¢¤®qÝ>6¼aªy·¢_­§Ê¼a¨V«f¥q°y±V¢¤­f¢-¬¼a±©¥q­f¨¸«k¦¹-®žªya¨¸«f¨V®ªy§-†û)«t¨Ÿ§Ä¨V²0¯/®ž­Ê«f¥qª¢«Z«f¡y¥.«Ÿ ¸ ·®{¢!§Zªa®ž«b¹®žª{ê¢-­f¬ž¢³«Ê®†-¢_­Ê®=«Ê®{®C­M¥qȳ¨Ÿ·±Ÿ¦;-í§Ê¨Vª+¹¢c¨¸«t«Ê¼a­fªy§®ž¼·«t«Ê¡+¥.«t«Ê¡a¨©§³¹®ž¼y±Ÿé«Ê¡a¢_ª6±Ÿ¢_¥žé«Ê®«Ê¡a¢¥q±Ÿ¬ž®­Ê¨V«Ê¡y²¬¢«T«f¨Vªy¬§k«f¼y¹MÒ=¨Ÿª¥c²0¨Ÿªa®ž­]²0®··¢®qÝO«Ê¡a¢³Ý€¼yªy¹X«f¨V®ªd¨¨L©š…c1ó,]q¼PT`bQ«f® ¯/¢-­ÊÝ€®ž­f² Ø µ Ø µ ¨Vª ¥öê@¥ž­Ê¨Ÿ¢«k¦ ®qݤ²0®··¢-±©§=¨©§C®qݹ®¼a­M§T¢é£†ýÁà )j£†¥@¦ž¢!§T¨©¥qª†¡a¢F²c®¢§k«C¯+®ā¼a±©¥q­ȳ­Ê®¬ž­M¥q²+ û)«]¡y¥ž§†°/¢-¢_ªìa¢-Ꞣ_±V®¯+¢!C¥q«†«Ê¡a¢Ø$ µ °y¨V®¢§k«M¥.«Ê¨©§T«Ê¨©¹-§†¼aªa¨V«Ä¥.«†«f¡a¢ýZªa¨Ÿêž¢_­f§Ê¨¸«k¦¨Ÿª·Ý€¢-­f¢-ªy¹-¢ýħʨVªa¬=Át¨Ÿ°a°y§Z÷¥ž²0ā±V¨Ÿªa¬µ ¥q²Â°y­Ê¨©·¬ž¢c¥qªy6¨¸«M§t­Ê¢!¹¢-ª¢«³êž¢_­f§Ê¨V®ªé¨©§t¹_¥q±Ÿ±V¢! B ¨Ÿªy£†ýÁÃ$ µ ®ª{Ꞣ-­f¬ž¢_ªy¹¢¤·¨Ÿ¥ž¬žªa®¢§k«f¨Ÿ¹_§§M¨)ā±V¼+§ZÝ€¼aª+¹X«Ê¨Ÿ®žª+§t«Ê¡y¥q«®qݵ îtËZÏù¥žªyF£ZîÄϤ k ®­²0®ž­f¢¤¨Ÿª·Ý€®ž­f²¥.«f¨V®ª §Ê¢-¢¥.«³«f¡a¢0Ð,¢_°Fȳ¥ž¬ž¢!§²¥@¦;-º®­³²0¥@¦6ªa®q«9-¨¥ž¹_¹®ž²0ȳ¥žª{¦é£ÑýtÁÃ6¥ž­Ê¢blP5P¥Ee{&ƒ5ƒ±»»m»eu.} y OD] G I9Heu0OqVÅ}˜uSVxO~uƒH m ƒ G H E Iqƒ³¥qª+íblP5PEv{&ƒ5ƒ±»m»»euÔEZH G F F OD]Lbxt5VFqPIbvuƒH F…Q »¡V1uStDU;H†ƒ GlQ V5ƒa¼ L Œ"!ÙG­Ó!Ù†¦g 9® '-Ž]¬t('ŒcŽ #‘¡'_Ž]½ L ‹ L ‹:LMK´¥[^]8`bc*¬g°­š]bYdcV[£†¥@¦¢_§Ê¨Ÿ¥žª ¥žāā­f®¥ž¹M¡ «f®é²0®{a¢-±†§T¢_±V¢!¹X«Ê¨Ÿ®žªÓȳ­Ê®·¹¢_¢_a§¤¥ž§¤Ý€®ž±Ÿ±V®.ÐZ§_éÃ{¼aā¯/®§Ê¢=«f¡y¥.«¤«Ê¡a¢ìa¥.«M¥Çl5¥ž­Ê¢=¹-®žªy§Ê¨Ÿa¢-­f¢_«Ê®¡y¥@ꢤ°/¢-¢_ªF¬¢-ªa¢_­f¥q«Ê¢!é°{¦6¥ì²0®{a¢-±_¾P-º®žªa¢0®žÝÑ¥§T¢-«¿®q݆¹®ž²0¯/¢«f¨Vªa¬²0®··¢-±©§_0Æ,¥ž¹M¡F²c®··¢_±I§T¯/¢_¹-¨Ê4+¢_§t«Ê¡y¢±Ó-b|g)rl} ¾Pv§n ° + ¥qȳ¥ž­T«ÑÝ€­Ê®² ¥qªC¼aªaÒ{ªa®.Ð]ªìȳ¥q­M¥q²0¢-«Ê¢-­ÑꞢ!¹X«f®ž­*n ° dÀ ° -·Ð]¡a¢_­Ê¢1À ° ¨Ÿ§Ñ«f¡a¢§T¢-«·¨©§k«f­Ê¨Ÿ°a¼·«f¨V®ªC®žÝ¢7É=¹¨Ÿ¢-ª¢«f§®qÝѲc®··¢_±+¾Fû)Ý¡£)¤¾ + ¨Ÿ§«Ê¡y¢cȳ­Ê¨Ÿ®ž­tā­f®ž°y¥ž°a¨V±Ÿ¨V«k¦ì®žÝ?²0®··¢-±+¾P-í«Ê¡a¢_ª®qÝÑ¥q±Ÿ±¦¯/®§f§Ê¨V°a±Ÿ¢cê@¥ž±V¼y¢_§Ý€®ž­«Ê¡a¢¹-®«Ê¡y¢¯+®¢§k«f¢-­f¨V®­Ñȳ­Ê®°y¥q°a¨Ÿ±Ÿ¨¸«k¦=¨©§†¬ž¨Ÿêž¢_ªC°{¦‚a) ¾=} l +v ¾ d¿ )Rž +£) ¾ + |g)l…} ¾ +¸=Á £) ¾ + |g)rl} ¾ +|g)l…} ¾ + ¨©§ì«Ê¡y¢Ó²0¥ž­Ê¬¨Vª+¥q±³±V¨ŸÒž¢_±V¨Ÿ¡a®{®·5¹_¥q±©¹¼a±©¥.«f¢_5¼y§Ê¨Vªa¬|)rl…} ¾ + o „ |g)l…} ¾˜vwn ° + £) n ° } ¾ +M‡ n ° ¥žªyÐ]¡a¢_­Ê¢° } ¾ + ¨©§†«f¡a¢¤¹®ªy·¨V«Ê¨Ÿ®žªy¥ž±íā­Ê¨Ÿ®ž­]·¨©§T«Ê­f¨V°a¼a«Ê¨Ÿ®žª®qÝ(n ° -{«f¡a¢²0®{a¢-±ºȳ¥ž­f¥ž²0¢«Ê¢_­f§,Ý€®­]²c®··¢_±-¾£)ƒnk ¨V­M§k«9-·¹-¥q±©¹¼y±Ÿ¥q«Ê¨Ÿ®žª®qݺ²¥ž­Ê¬¨Vªy¥ž±†¡a¢_­Ê¢Ä¥ž­Ê¢Z«kÐ,®¤²¥q»k®ž­?ȳ­Ê®°a±V¢_²§I¨Ÿª¹-¥ž±Ÿ¹-¼a±Ÿ¥q«Ê¨Ÿªa¬Â¯/®§T«Ê¢_­Ê¨Ÿ®ž­?²c®··¢_±+ȳ­Ê®°y¥q°a¨Ÿ±Ÿ¨¸«f¨V¢!§-²0¢-¢«M§«f¡a¢=¼y§Ê¼y¥q±?¨Vª¢«Ê¢_¬ž­M¥.«f¨V®ª;a¨ÊÉ=¹¼y±¸«f¨V¢!§Â·¢!§Ê¹-­Ê¨Ÿ°+¢! ¨Vªö§Ê¢_¹«Ê¨Ÿ®žªï‚žŸ‚žÃ{¢_¹-®žªy§-OÐ]¡a¢_ªÓÐ,¢=a¢_¥q±,Ð]¨¸«f¡±Ÿ¨VÒ¢-±Ÿ¨V¡a®{®·²¥qª{¦é²0®··¢-±©§¹-¥ž±Ÿ¹-¼a±©¥.«Ê¨Ÿ®žª ®qÝ|g)l…} ¾ + Ý€®­¤¥q±Ÿ±_¾0¿°/¢_¹-®ž²0¢_§³¨Ÿª·Ý€¢_¥§T¨Ÿ°a±Ÿ¢žØ µ Ø µ ²0¢«f¡a®·a§¤¹-¥žªF°/¢¼y§Ê¢Ý€¼a±¨ŸªÙ°+®ž«Ê¡6¹_¥ž§Ê¢_§Z§Ê¨Vª+¹¢«f¡a¢-¦·®=ªa®ž«Ä®žªy±V¦ìā­f®.ꢨ©·¢²0¢«f¡a®··®ž±Ÿ®ž¬¨V¢!§†Ý€®ž­¹-¥q±©¹¼y±Ÿ¥q«Ê¨Ÿªa¬«Ê¡y¢¤²¥q­f¬ž¨Ÿªy¥q±º±Ÿ¨ŸÒž¢-±Ÿ¨Ÿ¡a®{®{CÝ€­f®ž²µ Ø µ ®ž¼·«fā¼·«Ä°a¼a«]«Ê¡a¢_¦C¹-¥žªÙ¥q±©§T®cā­f®.ꢨ©·¢t«Ê®{®±Ÿ§†«f®¹®žª+§k«f­Ê¼y¹« ç÷±9Œ;‘7”Î7‘w²A,’wÛ0¥ž±V¬®ž­f¨¸«f¡a²§†Ð]¡a¨Ÿ¹M¡ì¬ž¢_ªa¢-­M¥.«f¢«Ê¡y¢¤Ø®ž°+§T¢_­Êê.¥.«f¨V®ªy§]Ý€­f®ž²ä«f¡a¢Ä»k®¨Vª¢«³¯+®¢§k«f¢-­f¨V®­·¨©§T«Ê­f¨V°a¼a«Ê¨Ÿ®žª$‚a) ¾˜vwn ° } l + ®qÝ) ¾˜vwn ° +B ¢0§T¡y¥ž±V±3·¢!¥q±¦Ð]¨¸«f¡é«Ê¡y¢_§Ê¢Â«kÐÑ®¹-¥§T¢!§†§T¢_ȳ¥q­M¥.«f¢-±Ÿ¦=¨VªC«Ê¡y¢ªa¢Ç{«]«kÐÑ®0§Ê¢_¹«Ê¨Ÿ®žªy§_