Asymptotics for a Bayesian nonparametric estimator of species richness.

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on clustering structure of the data. It has been recently shown that they can also be exploited in species sampling problems: they can be used for both modeling the random proportions of species within a population and making inference on various quantities of statistical interest. For applications involving large samples the exact evaluation of the corresponding estimators becomes impracticable and, therefore, asymptotic approximations are sought. In the present paper we study the limiting behaviour of the number of new species to be observed from further sampling, conditional on observed data, under a normalized generalized gamma process prior. Such an asymptotic study highlights the connections between the normalized generalized gamma process and the two-parameter Poisson-Dirichlet process, previously known only in the unconditional case.