Commission). We are very grateful to Andrew A. Scha ner for excellent research assistance. We thank Dr. Thomas F. Albert, Craig George and other scientists and personnel from the Borough's Department of Wildlife Management, the many other researchers with whom we have worked, most of whose names appear on papers in our reference list, the census crew, and the Eskimo hunters of the Borough, for their contributions to our understanding of bowhead whales and the census. We are also grateful to Geof Givens for useful discussions, and to Doug Butterworth and Andre Punt Estimating the population size and rate of increase of bowhead whales, Balaena mysticetus, is important because bowheads were the rst species of great whale for which commercial whaling stopped and so their status indicates the recovery prospects of other great whales, and also because this information is used by the International Whaling Commission (IWC) to set the aboriginal subsistence whaling quota for Alaskan Eskimos. We describe the 1993 visual and acoustic census o Point Barrow, Alaska, which provides the best data available for estimating these quantities. We outline the de nitive version of two statistical methods for estimating the population, the generalized removal method and the Bayes empirical Bayes

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.