SAMPLING MODELS WHICH ADMIT A GIVEN GENERAL EXPONENTIAL FAMILY AS A CONJUGATE FAMILY OF PRIORS

• 成果类型: Article
• 署名作者: BARLEV, SK; ENIS, P; LETAC, G
• 署名单位: State University of New York (SUNY) System; University at Buffalo, SUNY; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325643
• 发表日期: 1994
• 页码: 1555-1586
• 关键词: cubic variance functions; dispersion models

摘要

Let K = (K-lambda: lambda is an element of Lambda) be a family of sampling distributions for the data x on a sample space X which is indexed by a parameter lambda is an element of Lambda, and let F be a family of priors on Lambda. Then F is said to be conjugate for K if it is closed under sampling, that is, if the posterior distributions of lambda given the data x belong to F for almost all x. In this paper, we set up a framework for the study of what we term the dual problem: for a given family of priors F (a subfamily of a general exponential family), find the class of sampling models X for which F is conjugate. In particular, we show that K must be a general exponential family dominated by some measure and on (X, B), where B is the Borel field on X. It is the class of such measures and that we investigate in this paper. We study its geometric features and general structure and apply the results to some familiar examples.