Exchangeable partitions derived from Markovian coalescents

• 成果类型: Article
• 署名作者: Dong, Rui; Gnedin, Alexander; Pitman, Jim
• 署名单位: University of California System; University of California Berkeley; Utrecht University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000069
• 发表日期: 2007
• 页码: 1172-1201
• 关键词: sampling distributions; multiple collisions; neutral alleles; REPRESENTATION; CONVERGENCE; descent; mergers; models; lines

摘要

Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process and observed that similar methods could be applied to more complex models. Mohle described the recursion which determines the generalization of the Ewens sampling formula in the situation where the lines of descent are governed by a Lambda-coalescent, which allows multiple mergers. Here, we show that the basic integral representation of transition rates for the Lambda-coalescent is forced by sampling consistency under more general assumptions on the coalescent process. Exploiting an analogy with the theory of regenerative partition structures, we provide various characterizations of the associated partition structures in terms of discrete-time Markov chains.