Bayesian nonparametric inference for species variety with a two parameter Poisson-Dirichlet process prior

A Bayesian nonparametric methodology has been recently proposed in order to deal with the issue of prediction within species sampling problems. Such problems concern the evaluation, conditional on a sample of size n, of the species variety featured by an additional sample of size m. Genomic applications pose the additional challenge of having to deal with large values of both n and m. In such a case the computation of the Bayesian nonparametric estimators is cumbersome and prevents their implementation. In this paper we focus on the two parameter Poisson-Dirichlet model and provide completely explicit expressions for the corresponding estimators, which can be easily evaluated for any sizes of n and m. We also study the asymptotic behaviour of the number of new species conditionally on the observed sample: such an asymptotic result allows, combined with a suitable simulation scheme, to derive asymptotic highest posterior density intervals for the estimates of interest. Finally, we illustrate the implementation of the proposed methodology by the analysis of five Expressed Sequence Tags (EST) datasets.