Asymptotic approximations to the Bayes posterior risk

[摘要] Suppose that, givenω=(ω1,ω2)∈ℜ2,X1,X2,…andY1,Y2,…are independent random variables and their respective distribution functionsGω1andGω2belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities ofωlying 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 hypothesesH0:ω∈Ω1versusH1:ω∈Ω2using a zero-one loss function, whereΩ1andΩ2are disjoint closed convex subsets of the parameter space.

[学科分类] 应用数学