using tpa for bayesian inference

using tpa for bayesian inference

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時間：2018-02-11

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1、UsingTPAforBayesianInference*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587PublishedtoOxfordScholarshipOnline:January2012DOI

2、:10.1093/acprof:oso/9780199694587.001.0001UsingTPAforBayesianInference*MarkHuberSarahSchottDOI:10.1093/acprof:oso/9780199694587.003.0009AbstractandKeywordsFindingtheintegratedlikelihoodofamodelgiventhedatarequirestheintegrationofanonnegativefunctionovertheparameterspace.ClassicalMonteCarlomethod

3、sfornumericalintegrationrequireaboundorestimateofthevarianceinordertodeterminethequalityoftheoutput.Themethodcalledtheproductestimatordoesnotrequireknowledgeofthevarianceinordertoproducearesultofguaranteedquality,butrequiresacoolingschedulethatmusthavecertainstrictproperties.Findingacoolingsched

4、ulecanbedifficult,andfindinganoptimalcoolingscheduleisusuallycomputationallyoutofreach.TPAisamethodthatsolvesthisdifficulty,creatinganoptimalcoolingscheduleautomaticallyasitisrun.Thismethodhasitsownsetofrequirements;hereitisshownhowtomeettheserequirementsforproblemsarisinginBayesianinference.Thi

5、sgivesguaranteedaccuracyforintegratedlikelihoodsandPage1of31UsingTPAforBayesianInference*posteriormeansofnonnegativeparameters.Keywords:AdaptiveMonteCarlo,VarianceFreeApproximationSummaryFindingtheintegratedlikelihoodofamodelgiventhedatarequirestheintegrationofanonnegativefunctionovertheparamete

6、rspace.ClassicalMonteCarlomethodsfornumericalintegrationrequireaboundorestimateofthevarianceinordertodeterminethequalityoftheoutput.Themethodcalledtheproductestimatordoesnotrequireknowledgeofthevarianceinordertoproducearesultofguaranteedquality,butrequiresacoolingschedulethatmusthavecertainstric

7、tproperties.Findingacoolingschedulecanbedifficult,andfindinganoptimalcoolingscheduleisusuallycomputationallyoutofreach.TPAisamethodthatsolvesthisdifficulty,creatinganoptimalcoolingscheduleautomaticallyasitisrun.Thismethodhas

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