Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes

Abstract

The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters gets larger than 2 or 3 we propose two approximations for estimators of a particular parameter and compare their performance using examples.