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1、TowardsSmoothParticleFiltersforLikelihoodEstimationwithMultivariateLatentVariablesbyAnthonyLeeB.Sc.,TheUniversityofBritishColumbia,2006ATHESISSUBMITTEDINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEinTheFacultyofGraduateStudies(ComputerScience)THEUNIVERSITYOFBRITISHCOLU
2、MBIA(Vancouver)August,2008cAnthonyLee2008AbstractInparametrizedcontinuousstate-spacemodels,onecanobtainestimatesofthelikelihoodofthedatafor?xedparametersviatheSequentialMonteCarlomethodology.Unfortunately,evenifthelikelihoodiscontinuousintheparameters,theestimatesproducedbypracticalpartic
3、le?ltersarenot,evenwhencommonrandomnumbersareusedforeach?lter.Thisisbecausethesameresamplingstepwhichdrasticallyreducesthevarianceoftheestimatesalsointroducesdiscontinuitiesintheparticlesthatareselectedacross?lterswhentheparameterschange.Whenthestatevariablesareunivariate,themethodologyof
4、[23]givesanestimatorofthelog-likelihoodthatiscontinuousintheparameters.Wepresentanon-trivialgeneralizationofthismethodusingtree-basedo(N2)(andaslowasO(NlogN))resamplingschemesthatinducesigni?-cantcorrelationamongsttheselectedparticlesacross?lters.Inturn,thisreducesthevarianceofthedi?erenc
5、ebetweenthelikelihoodevaluatedfordi?erentvaluesoftheparametersandtheresultingestimatorisconsiderablysmootherthannaivelyrunningthe?lterswithcommonrandomnumbers.Importantly,inpracticeourmethodsrequireonlyachangetotheresampleoperationintheSMCframeworkwithouttheadditionofanyextraparametersand
6、canthereforebeusedforanyapplica-tioninwhichparticle?ltersarealreadyused.Inaddition,exceptingtheoptionaluseofinterpolationintheschemes,therearenoregularityconditionsfortheirusealthoughcertainconditionsmakethemmoreadvantageous.Inthisthesis,we?rstintroducetherelevantaspectsoftheSMCmethodolog
7、ytothetaskoflikelihoodestimationincontinuousstate-spacemodelsandpresentanoverviewofworkrelatedtothetaskofsmoothlikelihoodestimation.Followingthis,weintroducetheoreticallycorrectresamplingschemesthatcannotbeimplementedandthepracticaltree-basedresamplingschemesthatwer
