On Bayesian nonparametric inference for discovery probabilites

Given a sample of size $n$ from a population of species with unknown proportions, a common problem of  practical interest consists in making inference on the probability $D_{n}(l)$ that the $(n+1)$-th draw  coincides with a species with frequency $l$ in the sample, for any $l \geq 0$. Under the general framework  of Gibbs-type priors we show how to derive credible intervals for a Bayesian nonparametric estimator of  $D_{n}(l)$.