THE FORMAL DEFINITION OF REFERENCE PRIORS

• 成果类型: Article
• 署名作者: Berger, James O.; Bernardo, Jose M.; Sun, Dongchu
• 署名单位: Duke University; University of Missouri System; University of Missouri Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS587
• 发表日期: 2009
• 页码: 905-938
• 关键词: bayesian-analysis; posterior; distributions; probability; INFORMATION; CONVERGENCE; inference

摘要

Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. Reference priors have been rigorously defined in specific contexts and heuristically defined in general, but a rigorous general definition has been lacking. We produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions. The explicit expression can be used to derive new reference priors both analytically and numerically.