FREQUENTIST VALIDITY OF BAYESIAN LIMITS

• 成果类型: Article
• 署名作者: Kleijn, B. J. K.
• 署名单位: University of Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1952
• 发表日期: 2021
• 页码: 182-202
• 关键词: posterior distributions; convergence-rates; Consistency

摘要

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper, a Bayesian perspective on test sequences is proposed and Schwartz's Kullback-Leibler condition is generalised to widen the range of frequentist applications of posterior convergence. With Bayesian tests and a weakened form of contiguity termed remote contiguity, we prove simple and fully general frequentist theorems, for posterior consistency and rates of convergence, for consistency of posterior odds in model selection, and for conversion of sequences of credible sets into sequences of confidence sets with asymptotic coverage one. For frequentist uncertainty quantification, this means that a prior inducing remote contiguity allows one to enlarge credible sets of calculated, simulated or approximated posteriors to obtain asymptotically consistent confidence sets.