dc.contributor.author Frazier, David * dc.contributor.author Martin, Gael * dc.contributor.author Robert, Christian P. * dc.contributor.author Rousseau, Judith * dc.date.accessioned 2017-11-06T11:25:37Z dc.date.available 2017-11-06T11:25:37Z dc.date.issued 2018 dc.identifier.issn 0006-3444 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/16920 dc.language.iso en en dc.subject asymptotic properties dc.subject Bayesian consistency dc.subject Bernstein-von Mises theorem dc.subject likelihood-free methods dc.subject.ddc 519 en dc.title Asymptotic Properties of Approximate Bayesian Computation dc.type Article accepté pour publication ou publié dc.description.abstracten Approximate Bayesian computation (ABC) is becoming an accepted tool for statistical analysis in models with intractable likelihoods. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. In this paper we consider the asymptotic behavior of the posterior obtained from ABC and the ensuing posterior mean. We give general results on: (i) the rate of concentration of the ABC posterior on sets containing the true parameter (vector); (ii) the limiting shape of the posterior; and\ (iii) the asymptotic distribution of the ABC posterior mean. These results hold under given rates for the tolerance used within ABC, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that the required identification condition is far from guaranteed. The implications of the theoretical results for practitioners of ABC are also highlighted. dc.relation.isversionofjnlname Biometrika dc.relation.isversionofjnlvol 105 dc.relation.isversionofjnlissue 3 dc.relation.isversionofjnldate 2018 dc.relation.isversionofjnlpages 593-607 dc.relation.isversionofdoi 10.1093/biomet/asy027 dc.identifier.urlsite https://arxiv.org/abs/1607.06903 dc.relation.isversionofjnlpublisher Oxford University Press dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.description.ssrncandidate non dc.description.halcandidate non dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2018-11-16T14:55:27Z hal.person.labIds * hal.person.labIds * hal.person.labIds * hal.person.labIds *
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