INFERENCE FOR THE BINOMIAL N PARAlVIETER : A BAYES ElVIPIRICAL BAYES APPROACH

The problem of inference about the binomial N parameter is considered. Applications arise in situations where an unknown population size is to be estimated. Previous work has focused on point estimation, but many applications require interval estimation, prediction, and decision-making. A Bayes empirical Bayes approach is presented. This provides a simple and flexible way of specifying prior information, and also allows a convenient representation of vague prior knowledge. It yields solutions to the problems of interval estimation, prediction, and decision-making, as well as that of point estimation. The Bayes estimator compares favorably with the best, previously proposed, point estimators in the literature. The Bayesian estimation interval which corresponds to a vague prior distribution also performs satisfactorily when used as a frequentist confidence interval. Adrian E. Raftery is Associate Professor of Statistics and Sociology, University of Washington, Seattle, WA 98195. This work: was supported by ONR contract NOOO14-84-C-0169. I am grateful to W.S. Jewell for helpful discussions, and to George Casella, Peter Guttorp, n.v. Lindley, John Charles E. Smith, J. and Turet for comments on an earlier