Evaluation of Formal posterior distributions via Markov chain arguments

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dc.creatorEaton, Morris L.
dc.creatorHobert, James P.
dc.creatorJones, Galin L.
dc.creatorLai, Wen-Lin
dc.date2007-01-31
dc.date2008-11-05
dc.date.accessioned2026-07-07T10:16:55Z
dc.date.available2026-07-07T10:16:55Z
dc.descriptionWe consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function $ϕ$ of a parameter when the loss is quadratic. If the posterior mean of $ϕ$ is admissible for all bounded $ϕ$, the posterior is strongly admissible. We give sufficient conditions for strong admissibility. These conditions involve the recurrence of a Markov chain associated with the estimation problem. We develop general sufficient conditions for recurrence of general state space Markov chains that are also of independent interest. Our main example concerns the $p$-dimensional multivariate normal distribution with mean vector $θ$ when the prior distribution has the form $g(\|θ\|^2) dθ$ on the parameter space $\mathbb{R}^p$. Conditions on $g$ for strong admissibility of the posterior are provided.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS542 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0701938
dc.identifierhttp://arxiv.org/abs/math/0701938
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 5, 2423-2452
dc.identifierdoi:10.1214/07-AOS542
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173677
dc.subjectStatistics Theory
dc.subjectProbability
dc.subject62C15 (Primary) 60J05 (Secondary)
dc.titleEvaluation of Formal posterior distributions via Markov chain arguments
dc.typetext

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