# Bayesian nonparametric inference for discovery probabilities: credible intervals and large sample asymptotics

arXiv: https://arxiv.org/abs/1506.04915 · HTML: https://mlsanity.com/paper/1506.04915/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2015.

## Built on by (most cited first, 1 of 1)

- [Bayesian nonparametric estimation of coverage probabilities and distinct counts from sketched data](https://mlsanity.com/paper/2209.02135/) (2022)

## Abstract (arXiv)

Given a sample of size n from a population of individuals belonging to different species with unknown proportions, a popular problem of practical interest consists in making inference on the probability Dn(l) that the (n+1)-th draw coincides with a species with frequency l in the sample, for any l=0,1,ldots,n. This paper contributes to the methodology of Bayesian nonparametric inference for Dn(l). Specifically, under the general framework of Gibbs-type priors we show how to derive credible intervals for a Bayesian nonparametric estimation of Dn(l), and we investigate the large n asymptotic behaviour of such an estimator. Of particular interest are special cases of our results obtained under the specification of the two parameter Poisson--Dirichlet prior and the normalized generalized Gamma prior, which are two of the most commonly used Gibbs-type priors. With respect to these two prior specifications, the proposed results are illustrated through a simulation study and a benchmark Expressed Sequence Tags dataset. To the best our knowledge, this illustration provides the first comparative study between the two parameter Poisson--Dirichlet prior and the normalized generalized Gamma prior in the context of Bayesian nonparemetric inference for Dn(l).