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1、MarkovChainMonteCarloSimulationMethodsinEconometricsSiddharthaChibWashingtonUniversity,St.LouisMO,USAE-Mail:chib@simon.wustl.eduEdwardGreenbergWashingtonUniversity,St.LouisMO,USAE-Mail:edg@wuecona.wustl.eduFebruary,1995AbstractWepresentseveralMarkovchainMonteCarlosimulationmethod
2、sthathavebeenwidelyusedinrecentyearsineconometricsandstatistics.AmongtheseistheGibbssampler,whichhasbeenofparticularinteresttoeconometricians.Althoughthepapersummarizessomeoftherelevanttheoreticalliterature,itsemphasisisonthepresen-tationandexplanationofapplicationstoimportantmode
3、lsthatarestudiedinecono-metrics.Weincludeadiscussionofsomeimplementationissues,theuseofthemethodsinconnectionwiththeEMalgorithm,andhowthemethodscanbehelpfulinmodelspeci cationquestions.ManyoftheapplicationsofthesemethodsareofparticularinteresttoBayesians,butwealsopointoutwaysinwhi
4、chfrequentiststatisticiansmay ndthetechniquesuseful.Keywords:MarkovchainMonteCarlo,Gibbssampler,dataaugmentation,Metropolis-Hastingsalgorithm,MonteCarloEM,simulation.JELClassi cation:C11,C15,C20.Firstdraft:September28,1993;seconddraft:July1994.Weacknowledgetheveryhelpfulcommentso
5、fthreeanonymousreferees.11IntroductionInthispaperweexplainMarkovchainMonteCarlo(MCMC)methodsinsomedetailandillustratetheirapplicationtoproblemsineconometrics.Theseprocedures,whichenablethesimulationofalargesetofmultivariatedensityfunctions,haverevolutionizedthepracticeofBayesianst
6、atisticsandappeartobeapplicabletovirtuallyallparametriceconometricmodelsregardlessoftheircomplexity.Ourpurposeistoexplainhowthesemethodswork,bothintheoryandinpracticalapplications.SincemanyproblemsinBayesianstatistics(suchasthecomputationofposteriormomentsandmarginaldensityfunctio
7、ns)canbesolvedbysimulatingtheposteriordistribution,weemphasizeBayesianapplications,butthesetoolsarealsovaluableinfrequentistinference,wheretheycanbeusedtoexplorethelikelihoodsurfaceandto ndmodalestimatesormaximumlikelihoodestimateswith1di usepriors.AnMCMCmethodisasimulationtechniq
8、uethatgeneratesasample(multipleob
