Bayesian Nonparametric Estimation of the Probability of Discovering New Species

We consider the problem of evaluating the probability of discoveringa certain number of new species in a new sample of populationunits, conditional on the number of species recorded in a basicsample. We use a Bayesian nonparametric approach. The differentspecies proportions are assumed to be random and the observationsfrom the population exchangeable. We provide a Bayesian estimator,under quadratic loss, for the probability of discovering newspecies which can be compared with well-known frequentist estimators.The results we obtain are illustrated through a numerical exampleand an application to a genomic dataset concerning the discoveryof new genes by sequencing additional single-read sequencesof cdna fragments.