Afficher la notice abrégée

dc.contributor.authorHobert, James P.
dc.contributor.authorRobert, Christian P.
dc.date.accessioned2011-05-09T13:29:18Z
dc.date.available2011-05-09T13:29:18Z
dc.date.issued2004
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6227
dc.language.isoenen
dc.subjectBurn-inen
dc.subjectdrift conditionen
dc.subjectgeometric ergodicityen
dc.subjectKac’s theoremen
dc.subjectminorization conditionen
dc.subjectMultigamma Coupleren
dc.subjectRead-Once CFTPen
dc.subjectregenerationen
dc.subjectsplit chainen
dc.subject.ddc519en
dc.titleA mixture representation of π with applications in Markov chain Monte Carlo and perfect samplingen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenLet X={Xn:n=0,1,2,…} be an irreducible, positive recurrent Markov chain with invariant probability measure π. We show that if X satisfies a one-step minorization condition, then π can be represented as an infinite mixture. The distributions in the mixture are associated with the hitting times on an accessible atom introduced via the splitting construction of Athreya and Ney [Trans. Amer. Math. Soc. 245 (1978) 493–501] and Nummelin [Z. Wahrsch. Verw. Gebiete 43 (1978) 309–318]. When the small set in the minorization condition is the entire state space, our mixture representation of π reduces to a simple formula, first derived by Breyer and Roberts [Methodol. Comput. Appl. Probab. 3 (2001) 161–177] from which samples can be easily drawn. Despite the fact that the derivation of this formula involves no coupling or backward simulation arguments, the formula can be used to reconstruct perfect sampling algorithms based on coupling from the past (CFTP) such as Murdoch and Green’s [Scand. J. Statist. 25 (1998) 483–502] Multigamma Coupler and Wilson’s [Random Structures Algorithms 16 (2000) 85–113] Read-Once CFTP algorithm. In the general case where the state space is not necessarily 1-small, under the assumption that X satisfies a geometric drift condition, our mixture representation can be used to construct an arbitrarily accurate approximation to π from which it is straightforward to sample. One potential application of this approximation is as a starting distribution for a Markov chain Monte Carlo algorithm based on X.en
dc.relation.isversionofjnlnameThe Annals of Applied Probability
dc.relation.isversionofjnlvol14en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2004
dc.relation.isversionofjnlpages1295-1305en
dc.relation.isversionofdoihttp://dx.doi.org/10.1214/105051604000000305en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


Fichiers attachés à cette notice

FichiersTailleFormatConsulter

Il n'y a pas de fichiers associés à cette notice.

Ce document fait partie de la (des) collection(s) suivante(s)

Afficher la notice abrégée