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VOL. 6 | 2010 High dimensional Bernstein-von Mises: simple examples
Iain M. Johnstone

Editor(s) James O. Berger, T. Tony Cai, Iain M. Johnstone


In Gaussian sequence models with Gaussian priors, we develop some simple examples to illustrate three perspectives on matching of posterior and frequentist probabilities when the dimension p increases with sample size n: (i) convergence of joint posterior distributions, (ii) behavior of a non-linear functional: squared error loss, and (iii) estimation of linear functionals. The three settings are progressively less demanding in terms of conditions needed for validity of the Bernstein-von Mises theorem.


Published: 1 January 2010
First available in Project Euclid: 26 October 2010

MathSciNet: MR2798513

Digital Object Identifier: 10.1214/10-IMSCOLL607

Primary: 62E20
Secondary: 62F15

Keywords: frequentist , Gaussian sequence , High dimensional inference , linear functional , posterior distribution , squared error loss

Rights: Copyright © 2010, Institute of Mathematical Statistics


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