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Media type:
E-Article
Title:
ADAPTIVE BERNSTEIN–VON MISES THEOREMS IN GAUSSIAN WHITE NOISE
Contributor:
Ray, Kolyan
imprint:
Institute of Mathematical Statistics, 2017
Published in:The Annals of Statistics
Language:
English
ISSN:
0090-5364
Origination:
Footnote:
Description:
<p>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.</p>