Adaptive Bernstein–von Mises theorems in Gaussian white noise
File(s)
Accepted version
OA Location
Author(s)
Ray, Kolyan
Type
Journal Article
Abstract
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.
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.
Date Issued
2017-12-01
Date Acceptance
2016-12-06
Citation
Annals of Statistics, 2017, 45 (6), pp.2511-2536
ISSN
0090-5364
Publisher
Institute of Mathematical Statistics
Start Page
2511
End Page
2536
Journal / Book Title
Annals of Statistics
Volume
45
Issue
6
Copyright Statement
© Institute of Mathematical Statistics, 2017
Identifier
https://projecteuclid.org/euclid.aos/1513328581
Subjects
0102 Applied Mathematics
0104 Statistics
1403 Econometrics
Statistics & Probability
Publication Status
Published
Date Publish Online
2017-12-15