EVALUATION OF FORMAL POSTERIOR DISTRIBUTIONS VIA MARKOV CHAIN ARGUMENTS

• 成果类型: Article
• 署名作者: Eaton, Morris L.; Hobert, James P.; Jones, Galin L.; Lai, Wen-Lin
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; University of Florida; Providence University - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS542
• 发表日期: 2008
• 页码: 2423-2452
• 关键词: Admissibility

摘要

We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function phi of a parameter when the loss is quadratic. If the posterior mean of 0 is admissible for all bounded phi, 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 0 when the prior distribution has the form g(parallel to theta parallel to(2)) d theta on the parameter space RP. Conditions on g for strong admissibility of the posterior are provided.