A Class of Normalized Random Measures with an Exact Predictive Sampling Scheme

In this article, we define and investigate a novel class of nonparametric prior distributions, termed the class C. Such class of priors is dense with respect to the homogeneous normalized random measures with independent increments and it is characterized by a richer predictive structure than those arising from other widely used priors. Our interest in the class C is mainly motivated by Bayesian nonparametric analysis of some species sampling problems concerning the evaluation of the species relative abundances in a population. We study both the probability distribution of the number of species present in a sample and the probability of discovering a new species conditionally on an observed sample. Finally, by using the coupling from the past method, we provide an exact sampling scheme for the system of predictive distributions characterizing the class C.