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1、MCMCAppl.Bayes1MarkovChainMonteCarloandAppliedBayesianStatistics:ashortcourseChrisHolmesProfessorofBiostatisticsOxfordCentreforGeneFunctionMCMCAppl.Bayes2ObjectivesofCourse±TointroducetheBayesianapproachtostatisticaldatamodelling±TodiscussMarkovchainMo
2、nteCarlo(MCMC),astochasticsimulationtechniquethatisextremelyusefulforcomputinginferentialquantities.±Tointroducethesoftwarepackage“WinBugs”,atoolforsettingupBayesianmodelsandperforminginferenceviaMCMCMCMCAppl.Bayes3KeyReferences:Gelman,A.etal.BayesianD
3、ataAnalysis.2ndEd.(2004).Chapman&HallRobert,C.P.andCasella,G.MonteCarloStatisticalMethods.(2004/1999).SpringerGilks,W.R.etal.eds.MarkovchainMonteCarloinPractice.(1996).Chapman&Hall.Acknowledgements:NickyBestforWinBugshelpandexamples.MCMCAppl.Bayes41Int
4、roductionandextendedoverviewBayesianmethodsarebecomingincreasinglypopularastechniquesformodelling“systems”.AttheheartofBayesianproceduresisthefollowingphilosophy:Bayesianinferenceisaboutthequantificationandpropagationofuncertainty,definedviaaprobability,
5、inlightofobservationsofthesystem.FromPrior!Posterior.ThisisfundamentallydifferenttoclassicalinferencewhichtendstobeconcernedwithparameterestimationMostclassicalmodelscanbecastinaBayesianframework,forexample,normallinearregression,ARMA,GLMs,etcIntro5Asp
6、ectsofBayesthatpeoplelike±Uncertaintypropagation–Quantifyallaspectsofuncertaintyviaprobability.–Probabilityisthecentraltool.±Axiomatic–Bayesianstatisticshasanaxiomaticfoundation,fromwhichallproceduresthenfollow.–Itisprescriptiveintellingyouhowtoactcohe
7、rently–“Ifyoudon’tadoptaBayesianapproachyoumustaskyourselfwhichoftheaxiomsareyoupreparedtodiscard?”Seedisadvantages.±EmpiricalevidenceofeffectivenessIntro6–ThereismountingevidencethatBayesianproceduresoftenleadtomoreaccuratemodels,intermsofpredictivepe
8、rformance,thannon-Bayesapproaches.–Especiallytrueforcomplex(highlyparameterised)models.±Unifiedframework.–Randomeffects,Hierarchicalmodels,Missingvariables,NestedandNon-nestedmodels.Allhandledinthesameframework.±Intuitive–Foramodelparame