Species sampling models: consistency for the number of species

• 成果类型: Article
• 署名作者: Bissiri, P. G.; Ongaro, A.; Walker, S. G.
• 署名单位: University of Milano-Bicocca; University of Kent
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast006
• 发表日期: 2013
• 页码: 771777
• 关键词: nonparametric bayesian-inference; probability; richness; population; estimators; size

摘要

This paper considers species sampling models using constructions that arise from Bayesian nonparametric prior distributions. A discrete random measure, used to generate a species sampling model, can have either a countable infinite number of atoms, which has been the emphasis in the recent literature, or a finite number of atoms K, while allowing K to be assigned a prior probability distribution on the positive integers. It is the latter class of model we consider here, due to the interpretation of K as the number of species. We demonstrate the consistency of the posterior distribution of K as the sample size increases.