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August 2015 Frequentist coverage of adaptive nonparametric Bayesian credible sets
Botond Szabó, A. W. van der Vaart, J. H. van Zanten
Ann. Statist. 43(4): 1391-1428 (August 2015). DOI: 10.1214/14-AOS1270

Abstract

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of prescribed posterior probability in the posterior distribution of the chosen regularity. We show that such an adaptive Bayes credible set gives correct uncertainty quantification of “polished tail” parameters, in the sense of high probability of coverage of such parameters. On the negative side, we show by theory and example that adaptation of the prior necessarily leads to gross and haphazard uncertainty quantification for some true parameters that are still within the hyperrectangle regularity scale.

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Botond Szabó. A. W. van der Vaart. J. H. van Zanten. "Frequentist coverage of adaptive nonparametric Bayesian credible sets." Ann. Statist. 43 (4) 1391 - 1428, August 2015. https://doi.org/10.1214/14-AOS1270

Information

Received: 1 November 2013; Revised: 1 April 2014; Published: August 2015
First available in Project Euclid: 17 June 2015

zbMATH: 1317.62040
MathSciNet: MR3357861
Digital Object Identifier: 10.1214/14-AOS1270

Subjects:
Primary: 62G05, 62G15
Secondary: 62G20

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 4 • August 2015
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