ON THE BERNSTEIN-VON MISES PHENOMENON FOR NONPARAMETRIC BAYES PROCEDURES

• 成果类型: Article
• 署名作者: Castillo, Ismael; Nickl, Richard
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1246
• 发表日期: 2014
• 页码: 1941-1969
• 关键词: gaussian white-noise; posterior distributions; density; THEOREM; models; regression; extremes

摘要

We continue the investigation of Bernstein- von Mises theorems for non-parametric Bayes procedures from [Ann. Statist. 41 (2013) 1999-2028]. We introduce multiscale spaces on which nonparametric priors and posteriors are naturally defined, and prove Bernstein- von Mises theorems for a variety of priors in the setting of Gaussian nonparametric regression and in the i.i.d. sampling model. From these results we deduce several applications where posterior-based inference coincides with efficient frequentist procedures, including Donsker- and Kolmogorov-Smimov theorems for the random posterior cumulative distribution functions. We also show that multiscale posterior credible bands for the regression or density function are optimal frequentist confidence bands.