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August 2020 Asymptotic frequentist coverage properties of Bayesian credible sets for sieve priors
Judith Rousseau, Botond Szabo
Ann. Statist. 48(4): 2155-2179 (August 2020). DOI: 10.1214/19-AOS1881

Abstract

We investigate the frequentist coverage properties of (certain) Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To overcome this problem (in context of sieve type of priors), we introduce an extra assumption on the functional parameters, the so-called “general polished tail” condition. We then show that under standard assumptions, both the hierarchical and empirical Bayes methods, result in honest confidence sets for sieve type of priors in general settings and we characterize their size. We apply the derived abstract results to various examples, including the nonparametric regression model, density estimation using exponential families of priors, density estimation using histogram priors and the nonparametric classification model, for which we show that their size is near minimax adaptive with respect to the considered specific pseudometrics.

Citation

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Judith Rousseau. Botond Szabo. "Asymptotic frequentist coverage properties of Bayesian credible sets for sieve priors." Ann. Statist. 48 (4) 2155 - 2179, August 2020. https://doi.org/10.1214/19-AOS1881

Information

Received: 1 January 2018; Revised: 1 June 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134790
Digital Object Identifier: 10.1214/19-AOS1881

Subjects:
Primary: 62G05, 62G20
Secondary: 62G07, 62G08

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 4 • August 2020
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