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August 2007 Exchangeable partitions derived from Markovian coalescents
Rui Dong, Alexander Gnedin, Jim Pitman
Ann. Appl. Probab. 17(4): 1172-1201 (August 2007). DOI: 10.1214/105051607000000069

Abstract

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. Möhle described the recursion which determines the generalization of the Ewens sampling formula in the situation where the lines of descent are governed by a Λ-coalescent, which allows multiple mergers. Here, we show that the basic integral representation of transition rates for the Λ-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.

Citation

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Rui Dong. Alexander Gnedin. Jim Pitman. "Exchangeable partitions derived from Markovian coalescents." Ann. Appl. Probab. 17 (4) 1172 - 1201, August 2007. https://doi.org/10.1214/105051607000000069

Information

Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1147.60022
MathSciNet: MR2344303
Digital Object Identifier: 10.1214/105051607000000069

Subjects:
Primary: 60G09
Secondary: 60C05

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 4 • August 2007
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