ASIS算法是否应该广泛采用？.pdf

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1、应用概率统计第三十卷第一期2014年2月ChineseJournalofAppliedProbabilityandStatisticsVb1．30No．1Feb．2014Should、UseASIS?LIUJUN(Di"isi。nStatistics，NorthernIllinoisUniversity，DeKalb，儿60115,USA)SUNDONGCHU(SchoolofFinance。ndSt。tistics，EastChin。NormalUniversity，Sh。nghai，200241)(DepartmentofStatistics，U

2、niversityofMissouri，Columbia，MO65211，USA)AbstractThispaperimprovestheconvergenceoftwovarianceparametersinHeandSun(2000)byapplyingtheancillarity—suficiencyinterweavingstrategy(ASISinYuandMeng(2011))algorithmtotheGibbssamplingsteps．TheperformanceoftheASISalgorithmiscomparedwithth

3、eregularGibbssamplingbythepotentialscalereductionfactor，traceplotsandposteriorestimates．Theconvergenceofoneparameterimprovesgreatly,buttheotheronedoesnothaveaverysignificantimprovement．However，theoverallsamplingperformancehasimprovedgreatlysinceitneedsmuchfeweriterationsthanusi

4、ngregularGibbssamplingtoachi@veconvergence．Keywords：Ancillarity—suficiencyinterweavingstrategy,Bayesiancomputation，conditionalposteriordensity,GibbsSampling，MCMC，potentialscalereductionfactor．AMSSubjectClassification：62F15．§1．IntroductionAsthedevelopmentofcomputingtechnology,th

5、eMarkovchainMonteCarlo(MCM—C)methodhasbeenapowerfultoolinBayesiancomputation．However，MCMCalgorithmappliedtocomplicatedmodelsmayresultinslowconvergence．Forinstance，inhierarchi—calgeneralizedlinearmixedmodels，wherecomplexposteriordensitiesexist，theGibbssampling(GelfandandSmith，19

6、90)ofsomespecificparametersmayconvergeveryslowly．Manyresearchershavebeenworkingonimprovingit．YuandMeng(2011)proposedanancillarity—suficiencyinterweavingstrategy(ASIS)whichsignificantlybooststheMCMCeficiency．Thestrategyisusedtosampletheparameter0=(01．，Oj)fromaposteriordistributi

7、onp(olYob)。(p(YobIO)p(O)，’TheresearchWaSsupportedbytheUSNationalScienceFoundation(DMS．1007874，SES-1024080andSES-1260806)，theNaturalScienceFoundationofChina(11271136)andChinese111Project(B14019)．ReceivedSeptember19，2012．RevisedSeptember10，2013．doi：10．3969／j．issn．1001-4268．2014．0

8、1-0012应用概率统计第三十卷wherep(Yob8l0)isthelikelihoodandp(o)is