2014/07/31 by Kolyan Ray · 55 citations
Computer Science · Engineering · Mathematics · #Applied mathematics #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Finite element method #Frequentist inference #Gaussian #Hilbert space #Mathematical analysis #Mathematics #Reproducing kernel Hilbert space #Reservoir Engineering and Simulation Methods #Statistical Methods and Inference #Statistics #White noise #math.ST #msc:62G20 #stat.TH #von Mises distribution #von Mises yield criterion
paper · pdf · doi:10.1214/16-aos1533
published in The Annals of Statistics 45(6) (Institute of Mathematical Statistics) · 48 pages, 5 figures
arxiv created 2016/12/19 · openalex publication_date 2017/12/01 · arxiv updated 2017/12/21 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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 L2 and L∞, 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.