Restricted Bayes Estimates for Binomial Parameters

Abstract

Let θ = (θ_1,...,θ_k) be the parameters for k independent binomial random variables. We wish to estimate θ under the restriction θ ∊ R where R is a k-dimensional subset of the full parameter space {θ; 0 ≤ θ_i ≤ 1, i = 1,...,k}. Bayes estimators (means of posteriors) are developed for θ which correspond to prior distributions that assign probability one to the set R. Since the support of the resulting posterior is R, the posterior mean will be in R if R is a convex set. A bioassay example is given where the parameters are assumed to be increasing, or increasing and S-shaped.

This research was partially supported by an NSERC grant from the Canadian government while the author was a visiting professor in the Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario.