On the Bernstein-von Mises phenomenon in the Gaussian white noise model

H. Leahu

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Scopus)
107 Downloads (Pure)

Abstract

We study the Bernstein-von Mises (BvM) phenomenon, i.e., Bayesian credible sets and frequentist confidence regions for the estimation error coincide asymptotically, for the infinite-dimensional Gaussian white noise model governed by Gaussian prior with diagonal-covariance structure. While in parametric statistics this fact is a consequence of (a particular form of) the BvM Theorem, in the nonparametric setup, however, the BvM Theorem is known to fail even in some, apparently, elementary cases. In the present paper we show that BvM-like statements hold for this model, provided that the parameter space is suitably embedded into the support of the prior. The overall conclusion is that, unlike in the parametric setup, positive results regarding frequentist probability coverage of credible sets can only be obtained if the prior assigns null mass to the parameter space.
Original languageEnglish
Pages (from-to)373-404
JournalElectronic Journal of Statistics
Volume5
DOIs
Publication statusPublished - 2011

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