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August 2014 Markov jump processes in modeling coalescent with recombination
Xian Chen, Zhi-Ming Ma, Ying Wang
Ann. Statist. 42(4): 1361-1393 (August 2014). DOI: 10.1214/14-AOS1227

Abstract

Genetic recombination is one of the most important mechanisms that can generate and maintain diversity, and recombination information plays an important role in population genetic studies. However, the phenomenon of recombination is extremely complex, and hence simulation methods are indispensable in the statistical inference of recombination. So far there are mainly two classes of simulation models practically in wide use: back-in-time models and spatially moving models. However, the statistical properties shared by the two classes of simulation models have not yet been theoretically studied. Based on our joint research with CAS-MPG Partner Institute for Computational Biology and with Beijing Jiaotong University, in this paper we provide for the first time a rigorous argument that the statistical properties of the two classes of simulation models are identical. That is, they share the same probability distribution on the space of ancestral recombination graphs (ARGs). As a consequence, our study provides a unified interpretation for the algorithms of simulating coalescent with recombination, and will facilitate the study of statistical inference on recombination.

Citation

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Xian Chen. Zhi-Ming Ma. Ying Wang. "Markov jump processes in modeling coalescent with recombination." Ann. Statist. 42 (4) 1361 - 1393, August 2014. https://doi.org/10.1214/14-AOS1227

Information

Published: August 2014
First available in Project Euclid: 25 June 2014

zbMATH: 1319.60163
MathSciNet: MR3226160
Digital Object Identifier: 10.1214/14-AOS1227

Subjects:
Primary: 60J25 , 65C60
Secondary: 60J75 , 92B15 , 92D25

Keywords: ancestral recombination graph , back-in-time algorithm , Coalescent process , conditional distribution , Genetic recombination , Markov jump process , random sequence , spatial algorithm

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 4 • August 2014
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