Bayesian prediction with approximate frequentist validity

• 成果类型: Article
• 署名作者: Datta, GS; Mukerjee, R; Ghosh, M; Sweeting, TJ
• 署名单位: University System of Georgia; University of Georgia; State University System of Florida; University of Florida; Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; University of Surrey
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1414-1426
• 关键词: noninformative priors; posterior quantiles; bartlett correction; distributions; statistics; inference; parameter; intervals; regions

摘要

We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering both posterior quantiles and highest predictive density regions with reference to a future observation. The resulting priors are shown to be invariant under reparameterization. The role of Jeffreys' prior in this regard is also investigated. It is further shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched.