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1、IEEETRANSACTIONSONSIGNALPROCESSING,VOL.47,NO.10,OCTOBER19992667JointBayesianModelSelectionandEstimationofNoisySinusoidsviaReversibleJumpMCMCChristopheAndrieuandArnaudDoucetAbstractÐInthispaper,theproblemofjointBayesianmodelestimator[22],[24].However,in
2、practice,therearenumerousselectionandparameterestimationforsinusoidsinwhiteGauss-applicationswherethisnumberisunknownandhastobeiannoiseisaddressed.AnoriginalBayesianmodelisproposedestimated[13].TheuseofAICandMDLrequiresreliablethatallowsustodefineaposte
3、riordistributionontheparameterproceduresforMLparameterestimationforeachpossiblespace.AllBayesianinferenceisthenbasedonthisdistribution.Unfortunately,adirectevaluationofthisdistributionandofmodelandtheevaluationofthecriteria.Experimentalevidenceitsfeatu
4、res,includingposteriormodelprobabilities,requiresshowsthatAICandMDL,whicharecriteriadesignedusingevaluationofsomecomplicatedhigh-dimensionalintegrals.Weasymptoticarguments,doindeedtendtoestimateawrongdevelopanefficientstochasticalgorithmbasedonreversibl
5、ejumpnumberofcomponentsforasmallsamplesizeandalowMarkovchainMonteCarlomethodstoperformtheBayesiancomputation.Aconvergenceresultforthisalgorithmisestab-signal-to-noiseratio;see[13,Sec.VI].lished.Insimulation,itappearsthattheperformanceofdetectionWefollo
6、waBayesianapproachwherebytheunknownbasedonposteriormodelprobabilitiesoutperformsconventionalparameters,includingtheamplitudes,theradialfrequencies,detectionschemes.andthenoisevariance,togetherwiththenumberofsinusoids,IndexTermsÐBayesianmethods,MCMC,mod
7、elselection,areregardedasrandomquantitieswithknownpriordistri-spectralanalysis.bution.Severalpreviousworkshavealreadyaddressedthisproblem,insomerestrictedscenarios,followingtheBayesianapproach.BayesianparameterestimationandmodelselectionI.INTRODUCTIONf
8、orsuchsignalshavebeenaddressedinaseriesofpapersODELselectionisafundamentaldataanalysistask.ItbyBretthorst[8]±[10]and,morerecently,in[14]and[15].MhasmanyapplicationsinvariousfieldsofscienceandIn[12],theproblemofpowerspectrumestimationinth
