2007/01/31 by Morris L. Eaton, James P. Hobert, Galin L. Jones +1 · 3 citations
Computer Science · Mathematics · #Applied mathematics #Bayesian Methods and Mixture Models #Bayesian probability #Bounded function #Combinatorics #Context (archaeology) #Distribution (mathematics) #Markov chain #Mathematical analysis #Mathematics #Multivariate normal distribution #Multivariate statistics #Posterior probability #Prior probability #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics #math.PR #math.ST #msc:60J05 #msc:62C15 #stat.TH
paper · pdf · doi:10.1214/07-aos542
published in The Annals of Statistics 36(5) (Institute of Mathematical Statistics) · Published 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)
openalex publication_date 2008/10/01 · arxiv created 2008/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We 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 ℝp. Conditions on g for strong admissibility of the posterior are provided.