Large deviations associated with poisson-dirichlet distribution and ewens sampling formula

• 成果类型: Article
• 署名作者: Feng, Shui
• 署名单位: McMaster University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000230
• 发表日期: 2007
• 页码: 1570-1595
• 关键词: random discrete-distributions; alleles diffusion-model; fleming-viot process; neutral-alleles; selection; Mutation; size

摘要

Several results of large deviations are obtained for distributions that are associated with the Poisson-Dirichlet distribution and the Ewens sampling formula when the parameter theta approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of theta going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of theta going to infinity in a Poisson-Dirichlet distribution corresponds to a finite allele model where the mutation rate per individual is fixed and the number of alleles going to infinity. We call this the finite allele approximation. The first main result of this article is concerned with the relation between this finite allele approximation and the Poisson-Dirichlet distribution in terms of large deviations. Large theta can also be viewed as a limiting procedure of the effective population size going to infinity. In the second result a comparison is done between the sample size and the effective population size based on the Ewens sampling formula.