Bayesian Estimation of Population Diversity

• Activity Number: 479
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: International Society of Bayesian Analysis
• Author(s): John A Bunge*+
• Companies: Cornell University
• Keywords: species ; richness ; recapture ; diversity

Abstract

We consider estimating the number of species or other taxa in a closed population. This is similar and for some models equivalent to estimating the total size of a population (the capture-recapture problem). The history of research in this area has included parametric and nonparametric approaches, both informative and noninformative (or subjective and objective). Ordinarily we think of the problem as having two aspects: (i) estimating the parameter of interest, namely the total diversity (number of species or population size), while (ii) dealing with some collection of nuisance parameters (or a nonparametric version thereof) representing unobserved heterogeneity in abundances or capture probabilities. There have been notable recent advances especially in objective Bayes approaches (Jeffreys and reference priors in particular), and we discuss these and try to situate them in a larger context, also noting practical issues of computation, model selection, etc. We also consider relationships with the thread of literature on urn models (estimating the number of colors), coupon-collector problems, and the like. Recent applied examples are drawn from analysis of microbial diversity.