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.
"Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes." Ann. Statist. 7 (3) 558 - 568, May, 1979. https://doi.org/10.1214/aos/1176344677