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April 2006 Misspecification in infinite-dimensional Bayesian statistics
B. J. K. Kleijn, A. W. van der Vaart
Ann. Statist. 34(2): 837-877 (April 2006). DOI: 10.1214/009053606000000029

Abstract

We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P0, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback–Leibler divergence with respect to P0. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, with special interest for infinite-dimensional models. These include Gaussian mixtures, nonparametric regression and parametric models.

Citation

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B. J. K. Kleijn. A. W. van der Vaart. "Misspecification in infinite-dimensional Bayesian statistics." Ann. Statist. 34 (2) 837 - 877, April 2006. https://doi.org/10.1214/009053606000000029

Information

Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1095.62031
MathSciNet: MR2283395
Digital Object Identifier: 10.1214/009053606000000029

Subjects:
Primary: 62F05, 62F15, 62G07, 62G08, 62G20

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 2 • April 2006
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