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1、IEEEWorkshoponStatisticalSignalProcessing(SSP2005),Bordeaux,France,July2005MODELINGNONSTATIONARYHIDDENSEMI-MARKOVCHAINSWITHTRIPLETMARKOVCHAINSANDTHEORYOFEVIDENCEWojciechPieczynskiINT/GET,DépartementCITI,CNRSUMR51579,rueCharlesFourier,91000Evry,FranceABS
2、TRACTone,areavailable,whichenablesunsupervisedestimationofXfromY.HiddenMarkovchains,enablingonetorecoverthehiddenClassically,HMC-INhavebeenextendedintwoprocessevenforverylargesize,arewidelyusedinvariousdirections:problems.Ontheonehand,ithasbeenrecently(
3、i)InHMC-INthehiddenchainXisaMarkovone,andestablishedthatwhenthehiddenchainisnotstationary,thusthesojourndurationdistributionineachstateistheuseofthetheoryofevidenceisequivalenttoconsiderexponential.Inhiddensemi-MarkovchainswithatripletMarkovchainandcani
4、mprovetheefficiencyofindependentnoise(HSMC-IN),whichformanextensionunsupervisedsegmentation.Ontheotherhand,hiddenofHMC-IN,thisdistributionisofanykind.HSMC-INaresemi-Markovchainscanalsobeconsideredasparticularusefulinmanysituations,asimagessequenceanalys
5、is[5],tripletMarkovchains.Theaimofthispaperistousethesespeechprocessing[6],orstilltrackingproblems[15],twopointssimultaneously.Consideringanonstationaryamongothers;hiddensemi-Markovchain,weshowthatitispossibleto(ii)morerecently,HMC-INhavebeenextendedtoc
6、onsidertwoauxiliaryrandomchainsinsuchawaythat“pairwiseMarkovchains”(PMC[9]),inwhichoneunsupervisedsegmentationofnonstationaryhiddensemi-directlyassumestheMarkovianityofZ=(X,Y)andinMarkovchainsisworkable.whichXisnolongernecessarilyaMarkovchain,andto“trip
7、letMarkovchains”(TMC[10,13]),inwhichoneintroducesathirdauxiliaryrandomchainU=(U,...,U)1n1.INTRODUCTIONandassumestheMarkovianityofthetripletT=(X,U,Y).WhentherandomvariablesU,...,UtakeLetZ=(X,Y),withX=(X,...,X),Y=(Y,...,Y)be1n1n1ntheirvaluesinadiscretefin
8、itespace,bothPMCandTMCtworandomchains,whereeachXtakesitsvaluesinistillenabletoestimateXfromYbyBayesianmethods.W={w1,...,wk}andeachYtakesitsvaluesinR.WeiLetusmentionthatTMCcanbealsousedwhenthethreewillsaythatZ=(X,Y)isaclassicalhid
