FREQUENTIST COVERAGE OF ADAPTIVE NONPARAMETRIC BAYESIAN CREDIBLE SETS

• 成果类型: Article
• 署名作者: Szabo, Botond; van der Vaart, A. W.; van Zanten, J. H.
• 署名单位: Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University; University of Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1270
• 发表日期: 2015
• 页码: 1391-1428
• 关键词: CONFIDENCE BANDS; Inverse problems; inference

摘要

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of prescribed posterior probability in the posterior distribution of the chosen regularity. We show that such an adaptive Bayes credible set gives correct uncertainty quantification of polished tail parameters, in the sense of high probability of coverage of such parameters. On the negative side, we show by theory and example that adaptation of the prior necessarily leads to gross and haphazard uncertainty quantification for some true parameters that are still within the hyperrectangle regularity scale.