Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 320--334

VARIATIONS OF POSTERIOR EXPECTATIONS FOR SYMMETRIC UNIMODAL PRIORS IN A DISTRIBUTION BAND

By

SANJIB BASU, University of Arkansas

SUMMARY. Given a random variable with distribution indexed by a one dimensional parameter q , we consider the problem of robustness of a given Bayesian posterior criterion when the prior c.d.f. lies in the class G SU= {F: FL F FU 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 a posterior expectation of function h(q ) as the prior varies in G SU. Finally, the method is illustrated with two examples. The use of this family in subjective prior elicitation is also discussed.

AMS (1990) subject classification. 62F15,62F35,62G35.

Key words and phrases. cdf, distribution band, symmetry, unimodal, prior, posterior, likelihood, robust-ness, range, Kolmogorov metric, Lévy metric.

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This article in mathematical reviews.