Asymptotic approximations to the Bayes posterior risk. (1990)

• Record Type: Journal Article
• Authors: Zoubeidi, Toufik
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 3:Number 2(1990)
• Page Start: 99
• Page End: 116
• Publication Date: 1990
• Subjects: exponential families of distributions Bayes risk -- testing hypotheses -- indifference zone; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953390000090
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Suppose that, given ω = ( ω 1, ω 2 ) ∈ ℜ 2, X 1, X 2, … and Y 1, Y 2, … are independent random variables and their respective distribution functions G ω 1 and G ω 2 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 H 0 : ω ∈ Ω 1 versus H 1 : ω ∈ Ω 2 using a zero-one loss function, where Ω 1 and Ω 2 are disjoint closed convex subsets of the parameter space.