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Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 2, Pages 99-116

Asymptotic approximations to the Bayes posterior risk

Department of Statistics, University of Rochester, Rochester 14627, NY, USA

Received 1 January 1990; Revised 1 March 1990

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Suppose that, given ω=(ω1,ω2)2, X1,X2, and Y1,Y2, are independent random variables and their respective distribution functions Gω1 and Gω2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω lying in closed convex subsets of the parameter space under a general prior density. Using this, we then approximate the Bayes posterior risk for testing the hypotheses H0:ωΩ1 versus H1:ωΩ2 using a zero-one loss function, where Ω1 and Ω2 are disjoint closed convex subsets of the parameter space.