Bayesian nonparametric inference on rare species variety

A Bayesian nonparametric methodology has been recently proposed for drawing inferences on the overall species variety in species sampling problems. In this paper we consider the practically important and technically challenging issue of estimating the rare species variety, namely the number of species with frequency less than a given threshold: specifically, adopting a two-parameter Poisson-Dirichlet process prior, we provide estimators for this and related quantities and study their properties. The methods are illustrated through an application on genomic data.