Bayesian non-parametric inference for species variety with a two-parameter Poisson-Dirichlet process prior

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2009-11, Vol.71 (5), p.993-1008
• Main Authors: Favaro, Stefano, Lijoi, Antonio, Mena, Ramsés H., Prünster, Igor
• Format: Article
• Language: English
• Subjects: Asymptotics; Bayesian analysis; Bayesian method; Bayesian non-parametrics; Datasets; Estimating techniques; Estimation; Estimators; Exact sciences and technology; Expressed sequence tags analysis; General topics; Genomics; Inference; Inference from stochastic processes; time series analysis; Libraries; Mathematical intervals; Mathematics; Maximum likelihood estimation; New species; Parametric inference; Point estimators; Posterior probability of discovering a new species; Probability and statistics; Probability theory and stochastic processes; Random variables; Sample coverage; Sampling; Sciences and techniques of general use; Species; Species sampling; Statistical methods; Statistics; Stochastic processes; Studies; Two-parameter Poisson-Dirichlet process
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2009.00717.x

A Bayesian non-parametric methodology has been recently proposed to deal with the issue of prediction within species sampling problems. Such problems concern the evaluation, conditional on a sample of size n, of the species variety featured by an additional sample of size m. Genomic applications pose the additional challenge of having to deal with large values of both n and m. In such a case the computation of the Bayesian non-parametric estimators is cumbersome and prevents their implementation. We focus on the two-parameter Poisson-Dirichlet model and provide completely explicit expressions for the corresponding estimators, which can be easily evaluated for any sizes of n and m. We also study the asymptotic behaviour of the number of new species conditionally on the observed sample: such an asymptotic result, combined with a suitable simulation scheme, allows us to derive asymptotic highest posterior density intervals for the estimates of interest. Finally, we illustrate the implementation of the proposed methodology by the analysis of five expressed sequence tags data sets.