The Annals of Statistics

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

Donald A. Berry and Ronald Christensen

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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.

Article information

Ann. Statist., Volume 7, Number 3 (1979), 558-568.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62F15: Bayesian inference 62F10: Point estimation

Empirical Bayes estimation Dirichlet processes mixtures of Dirichlet processes approximating mixtures of Dirichlet processes binomial parameter estimation


Berry, Donald A.; Christensen, Ronald. Empirical Bayes Estimation of a Binomial Parameter Via Mixtures of Dirichlet Processes. Ann. Statist. 7 (1979), no. 3, 558--568. doi:10.1214/aos/1176344677.

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