CONDITIONAL FORMULAE FOR GIBBS-TYPE EXCHANGEABLE RANDOM PARTITIONS

• 成果类型: Article
• 署名作者: Favaro, Stefano; Lijoi, Antonio; Prunster, Igor
• 署名单位: University of Turin; University of Pavia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP843
• 发表日期: 2013
• 页码: 1721-1754
• 关键词: indexes

摘要

Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we investigate some properties concerning the conditional distribution of the number of blocks with a certain frequency generated by Gibbs-type random partitions. The general results are then specialized to three noteworthy examples yielding completely explicit expressions of their distributions, moments and asymptotic behaviors. Such expressions can be interpreted as Bayesian nonparametric estimators of the rare species variety and their performance is tested on some real genomic data.