On the existence of inferences which are consistent with a given model

• 成果类型: Article
• 署名作者: Berti, P; Rigo, P
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1235-1249
• 关键词: finitely additive priors; statistical-inference; improper priors; coherent

摘要

If {p(theta)} is a sigma-additive statistical model and pi a finitely additive prior, then any statistic T is sufficient, with respect to a suitable inference consistent with {p(theta)} and pi, provided only that p(theta)(T = t) = 0 for all theta and t. Here, sufficiency is to be intended in the Bayesian sense, and consistency in the sense of Lane and Sudderth. As a corollary, if {p(theta)} is sigma-additive and diffuse, then, whatever the prior pi, there is an inference which is consistent with {p(theta)} and pi. Two versions of the main result are also obtained for predictive problems.