Conditional $\alpha$-diversity for exchangeable Gibbs partitions driven by the stable subordinator

TL;DR

This paper generalizes the asymptotic behavior of conditional alpha-diversity from specific models to a broader class of mixed Poisson-Kingman species sampling models driven by the stable subordinator, with implications for Bayesian species richness estimation.

Contribution

It extends previous results on alpha-diversity asymptotics to a larger class of models driven by the stable subordinator, broadening their applicability.

Findings

Generalized asymptotic results for conditional alpha-diversity.

Applied to mixed Poisson-Kingman models driven by the stable subordinator.

Enhanced understanding of species richness estimation in Bayesian frameworks.

Abstract

Asymptotic behaviour of conditional $\alpha$ diversity for the two-parameter Poisson-Dirichlet partition model and for the normalized generalized Gamma model has been recently investigated in Favaro et al. (2009, 2011) with a view to possible applications in Bayesian treatment of species richness estimation. Here we generalize those results to the larger class of mixed Poisson-Kingman species sampling models driven by the stable subordinator (Pitman, 2003).