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June, 1986 Robust Bayes and Empirical Bayes Analysis with $_\epsilon$-Contaminated Priors
James Berger, L. Mark Berliner
Ann. Statist. 14(2): 461-486 (June, 1986). DOI: 10.1214/aos/1176349933

Abstract

For Bayesian analysis, an attractive method of modelling uncertainty in the prior distribution is through use of $\varepsilon$-contamination classes, i.e., classes of distributions which have the form $\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, \pi_0$ being the base elicited prior, $q$ being a "contamination," and $\varepsilon$ reflecting the amount of error in $\pi_0$ that is deemed possible. Classes of contaminations that are considered include (i) all possible contaminations, (ii) all symmetric, unimodal contaminations, and (iii) all contaminations such that $\pi$ is unimodal. Two issues in robust Bayesian analysis are studied. The first is that of determining the range of posterior probabilities of a set as $\pi$ ranges over the $\varepsilon$-contamination class. The second, more extensively studied, issue is that of selecting, in a data dependent fashion, a "good" prior distribution (the Type-II maximum likelihood prior) from the $\varepsilon$-contamination class, and using this prior in the subsequent analysis. Relationships and applications to empirical Bayes analysis are also discussed.

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James Berger. L. Mark Berliner. "Robust Bayes and Empirical Bayes Analysis with $_\epsilon$-Contaminated Priors." Ann. Statist. 14 (2) 461 - 486, June, 1986. https://doi.org/10.1214/aos/1176349933

Information

Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0602.62004
MathSciNet: MR840509
Digital Object Identifier: 10.1214/aos/1176349933

Subjects:
Primary: 62A15
Secondary: 62F15

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June, 1986
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