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dc.contributor.authorAndrieu, Christophe
dc.contributor.authorLee, Anthony
dc.contributor.authorVihola, Matti
dc.date.accessioned2017-09-27T10:23:51Z
dc.date.available2017-09-27T10:23:51Z
dc.date.issued2018
dc.identifier.citationAndrieu, C., Lee, A., & Vihola, M. (2018). Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers. <i>Bernoulli</i>, <i>24</i>(2), 842-872. <a href="https://doi.org/10.3150/15-BEJ785" target="_blank">https://doi.org/10.3150/15-BEJ785</a>
dc.identifier.otherCONVID_27241862
dc.identifier.otherTUTKAID_75104
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/55459
dc.description.abstractWe establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers [J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 269–342]. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC Markov chain, as well as quantitative bounds on its (uniformly geometric) rate of convergence. Furthermore, we show that the i-cSMC Markov chain cannot even be geometrically ergodic if this essential boundedness does not hold in many applications of interest. Our sufficiency and quantitative bounds rely on a novel non-asymptotic analysis of the expectation of a standard normalizing constant estimate with respect to a “doubly conditional” SMC algorithm. In addition, our results for i-cSMC imply that the rate of convergence can be improved arbitrarily by increasing N, the number of particles in the algorithm, and that in the presence of mixing assumptions, the rate of convergence can be kept constant by increasing N linearly with the time horizon. We translate the sufficiency of the boundedness condition for i-cSMC into sufficient conditions for the particle Gibbs Markov chain to be geometrically ergodic and quantitative bounds on its geometric rate of convergence, which imply convergence of properties of the particle Gibbs Markov chain to those of its corresponding Gibbs sampler. These results complement recently discovered, and related, conditions for the particle marginal Metropolis–Hastings (PMMH) Markov chain.
dc.language.isoeng
dc.publisherInternational Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability
dc.relation.ispartofseriesBernoulli
dc.subject.othergeometric ergodicity
dc.subject.otheriterated conditional sequential Monte Carlo
dc.subject.otherMetropoliswithin-Gibbs
dc.subject.otherparticle Gibbs
dc.subject.otheruniform ergodicity
dc.titleUniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201709223796
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineTilastotiedefi
dc.contributor.oppiaineStatisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2017-09-22T09:15:06Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange842-872
dc.relation.issn1350-7265
dc.relation.numberinseries2
dc.relation.volume24
dc.type.versionpublishedVersion
dc.rights.copyright© 2018 ISI/BS. Published by International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber274740
dc.relation.doi10.3150/15-BEJ785
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramAkatemiatutkijan tehtävä, SAfi
jyx.fundingprogramResearch post as Academy Research Fellow, AoFen


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