Nonparametric bayes estimation of the probability of discovering a new species

Abstract

A random sample is taken from a population consisting of an unknown number of distinct species. The parameter of interest is the probability of discovering a new species when an additional draw from the population is made. Recently, Clayton and Frees (1987) introduced a new nonparametric estimator of this parameter as an alternative to Starr's (1979) minimum variance unbiased estimator. In this paper, the Bayes estimator of the parameter is derived using the Dirichlet process prior and the squared error loss function. The limiting Bayes estimator is shown to have asymptotically normal distribution. A Monte Carlo study of these estimators is provided, and their merits and shortcomings are discussed.