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October 2008 Evaluation of formal posterior distributions via Markov chain arguments
Morris L. Eaton, James P. Hobert, Galin L. Jones, Wen-Lin Lai
Ann. Statist. 36(5): 2423-2452 (October 2008). DOI: 10.1214/07-AOS542


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(‖θ2)  on the parameter space ℝp. Conditions on g for strong admissibility of the posterior are provided.


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Morris L. Eaton. James P. Hobert. Galin L. Jones. Wen-Lin Lai. "Evaluation of formal posterior distributions via Markov chain arguments." Ann. Statist. 36 (5) 2423 - 2452, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1274.62078
MathSciNet: MR2458193
Digital Object Identifier: 10.1214/07-AOS542

Primary: 62C15
Secondary: 60J05

Keywords: Admissibility , formal Bayes , Improper prior distribution , multivariate normal distribution , recurrence , superharmonic function

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • October 2008
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