ADAPTIVE BERNSTEIN-VON MISES THEOREMS IN GAUSSIAN WHITE NOISE

• 成果类型: Article
• 署名作者: Ray, Kolyan
• 署名单位: Leiden University; Leiden University - Excl LUMC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1533
• 发表日期: 2017
• 页码: 2511-2536
• 关键词: bayesian credible sets; self-similar functions; frequentist coverage; confidence bands; posterior concentration; DENSITY-ESTIMATION; Inverse problems; priors; regression; inference

摘要

We investigate Bernstein-von Mises theorems for adaptive nonparametric Bayesian procedures in the canonical Gaussian white noise model. We consider both a Hilbert space and multiscale setting with applications in L-2 and L-infinity, respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets based on the posterior distribution. We also provide simulations to numerically illustrate our approach and obtain a visual representation of the geometries involved.