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June, 1989 Ranges of Posterior Measures for Priors with Unimodal Contaminations
S. Sivaganesan, James O. Berger
Ann. Statist. 17(2): 868-889 (June, 1989). DOI: 10.1214/aos/1176347148

Abstract

We consider the problem of robustness or sensitivity of given Bayesian posterior criteria to specification of the prior distribution. Criteria considered include the posterior mean, variance and probability of a set (for credible regions and hypothesis testing). Uncertainty in an elicited prior, $\pi_0$, is modelled by an $\varepsilon$-contamination class $\Gamma = \{\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, q \in Q\}$, where $\varepsilon$ reflects the amount of probabilistic uncertainty in $\pi_0$, and $Q$ is a class of allowable contaminations. For $Q = \{$all unimodal distributions$\}$ and $Q = \{\text{all symmetric unimodal distributions}\}$, we determine the ranges of the various posterior criteria as $\pi$ varies over $\Gamma$.

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S. Sivaganesan. James O. Berger. "Ranges of Posterior Measures for Priors with Unimodal Contaminations." Ann. Statist. 17 (2) 868 - 889, June, 1989. https://doi.org/10.1214/aos/1176347148

Information

Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0724.62032
MathSciNet: MR994273
Digital Object Identifier: 10.1214/aos/1176347148

Subjects:
Primary: 62F15
Secondary: 62C10, 62F35

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • June, 1989
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