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

• 成果类型: Article
• 署名作者: Favaro, Stefano; Lijoi, Antonio; Mena, Ramses H.; Prunster, Igor
• 署名单位: Universidad Nacional Autonoma de Mexico; Collegio Carlo Alberto; University of Turin; University of Pavia; Consiglio Nazionale delle Ricerche (CNR); Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes (IMATI-CNR)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2009.00717.x
• 发表日期: 2009
• 页码: 993-1008
• 关键词: probability

摘要

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.