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1、MarkovChainMonteCarloMethodsforStatisticalInferenceJulianBesag1DepartmentofStatisticsUniversityofWashington,Seattle,USASpring2004SUMMARYThesenotesprovideanintroductiontoMarkovchainMonteCarlomethodsandtheirapplicationstobothBayesianandfrequentiststatisticalinference.Suchmeth
2、odshaverevolutionizedwhatcanbeachievedcomputationally,es-peciallyintheBayesianparadigm.Theaccountbeginsbydiscussingordi-naryMonteCarlomethods:thesehavethesamegoalsastheMarkovchainversionsbutcanonlyrarelybeimplemented.SubsequentsectionsdescribebasicMarkovchainMonteCarlo,base
3、dontheHastingsalgorithmandin-cludingboththeMetropolismethodandtheGibbssamplerasspecialcases,andgoontodiscusssomemorespecializeddevelopments,includingadaptiveslicesampling,exactgoodness{of{¯ttests,maximumlikelihoodestimation,theLangevin{Hastingsalgorithm,auxiliaryvariableste
4、chniques,perfectsam-plingviacouplingfromthepast,reversiblejumpsmethodsfortargetspacesofvaryingdimensions,andsimulatedannealing.Specimenapplicationsaredescribedthroughoutthenotes.Keywords:Adaptiveslicesampling;Autologisticdistribution;Auxiliaryvariables;Bayesiancompu-tation;
5、Competingrisks;Contingencytables;Darwin's¯nches;Exactp{values;Gibbssampler;Hastingsalgorithm;HiddenMarkovmodels;Importancesampling;Isingmodel;Langevindi®usion;MarkovchainMonteCarlo;Markovrandom¯elds;Maximumlikelihoodestimation;Metropolismethod;Mixturemod-els;Noisybinarychan
6、nel;Perfectsimulation;Pointprocesses;Raschmodel;Reversibility;Reversiblejumps;Simulatedannealing;Spatialstatistics;Swendsen{Wangalgorithm;Travelingsalesman;Weibulldistribution;Wol®'salgorithm.1Addressforcorrespondence:DepartmentofStatistics,UniversityofWashington,Box354322,
7、SeattleWA98195,USA;E-mail:julian@stat.washington.edu11Thecomputationalchallenge1.1IntroductionMorethan¯ftyyearsago,Metropolis,Rosenbluth,Rosenbluth,TellerandTeller(1953)in-troducedtheMetropolisalgorithmintothephysicsliterature.WiththenotableexceptionofHammersleyandHandscomb
8、(1964,Ch.9),therewaslittleinterestfromstatisticiansinsuchMarkovchainMonteCarlo(MCM
