Bayesian nonparametric estimation of Simpson's evenness index under $α-$Gibbs priors

Details Bayesian nonparametric estimation of Simpson's evenness index under $α-$Gibbs priors Bayesian nonparametric estimation of Simpson's evenness index under $α-$Gibbs priors

2012-03-08

arxiv.org/abs/1203.1666v1

Mathematics

Statistics Theory

12 pages

Scientific paper

A Bayesian nonparametric approach to the study of species diversity based on choosing a random discrete distribution as a prior model for the unknown relative abundances of species has been recently introduced in Lijoi et al. (2007, 2008). Explicit posterior predictive estimation of {\it species richness} has been obtained under priors belonging to the $\alpha$-Gibbs class (Gnedin & Pitman, 2006). Here we focus on posterior estimation of {\it species evenness} which accounts for diversity in terms of the proximity to the situation of uniform distribution of the population into different species. We focus on Simpson's index and provide a Bayesian estimator under quadratic loss function, with its variance, under some specific $\alpha-$Gibbs priors.

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