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Using a Markov Chain to Construct a Tractable Approximation of an Intractable Probability Distribution

dc.contributor.authorHobert, James P.
dc.contributor.authorJones, Galin L.
dc.contributor.authorRobert, Christian P.
dc.date.accessioned2011-05-09T08:46:14Z
dc.date.available2011-05-09T08:46:14Z
dc.date.issued2006
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6211
dc.language.isoenen
dc.subjectburn-inen
dc.subjectGibbs sampleren
dc.subjectminorization conditionen
dc.subjectmixture representationen
dc.subjectMonte Carloen
dc.subjectregenerationen
dc.subjectsplit chainen
dc.subject.ddc519en
dc.titleUsing a Markov Chain to Construct a Tractable Approximation of an Intractable Probability Distributionen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenLet π denote an intractable probability distribution that we would like to explore. Suppose that we have a positive recurrent, irreducible Markov chain that satisfies a minorization condition and has π as its invariant measure. We provide a method of using simulations from the Markov chain to construct a statistical estimate of π from which it is straightforward to sample. We show that this estimate is ‘strongly consistent’ in the sense that the total variation distance between the estimate and π converges to 0 almost surely as the number of simulations grows. Moreover, we use some recently developed asymptotic results to provide guidance as to how much simulation is necessary. Draws from the estimate can be used to approximate features of π or as intelligent starting values for the original Markov chain. We illustrate our methods with two examples.en
dc.relation.isversionofjnlnameScandinavian Journal of Statistics
dc.relation.isversionofjnlvol33en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2006
dc.relation.isversionofjnlpages37-51en
dc.relation.isversionofdoihttp://dx.doi.org/10.1111/j.1467-9469.2006.00467.xen
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherWileyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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