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Variations of Posterior Expectations for Symmetric Unimodal Priors in a Distribution Band

Sanjib Basu
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 56, No. 2 (Jun., 1994), pp. 320-334
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050991
Page Count: 15
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Variations of Posterior Expectations for Symmetric Unimodal Priors in a Distribution Band
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Abstract

Given a random variable with distribution indexed by a one dimensional parameter θ, we consider the problem of robustness of a given Bayesian posterior criterion when the prior c.d.f lies in the class $\Gamma _{SU}=\{F\colon F_{L}\leq F\leq F_{U}$ and F is symmetric and unimodal}. Such a class includes as special cases well known metric neighborhoods of a fixed c.d.f such as Kolmogorov and Lévy neighborhoods. A general method is described for finding the extremum of posterior expectation of a function h(θ) as the prior varies in $\Gamma _{SU}$. Finally, the method is illustrated with two examples. The use of this family in subjective prior elicitation is also discussed.

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