On some Bayesian nonparametric estimators for species richness under two-parameter Poisson-Dirichlet priors

TL;DR

This paper introduces a new Bayesian nonparametric method for estimating species richness using two-parameter Poisson-Dirichlet priors, simplifying proofs and providing a novel scale mixture representation of the asymptotic law.

Contribution

It offers an alternative approach leveraging deletion of classes property and Beta-Binomial results, enhancing simplicity and insight in species richness estimation.

Findings

Simplified proofs for Bayesian nonparametric estimators

New scale mixture representation of the asymptotic law

Enhanced understanding of species richness under Poisson-Dirichlet priors

Abstract

We present an alternative approach to the Bayesian nonparametric analysis of conditional species richness under two-parameter Poisson Dirichlet priors. We rely on a known characterization by deletion of classes property and on results for Beta-Binomial distributions. Besides leading to simplified and much more direct proofs, our proposal provides a new scale mixture representation of the conditional asymptotic law.