On a Markov chain related to the individual lengths in the recursive construction of Kingman’s coalescent

Yuan, Linglong ORCID: 0000-0002-7851-1631 (2024) On a Markov chain related to the individual lengths in the recursive construction of Kingman’s coalescent. Latin American Journal of Probability and Mathematical Statistics, 21 (1). p. 725. ISSN 1980-0436

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Abstract

Kingman’s coalescent is a widely used process to model sample genealogies in population genetics. Recently there have been studies on the inference of quantities related to the genealogy of additional individuals given a known sample. This paper explores the recursive (or sequential) construction which is a natural way of enlarging the sample size by adding individuals one after another to the sample genealogy via individual lineages to construct Kingman’s coalescent. Although the process of successively added lineage lengths is not Markovian, we show that it contains a Markov chain which records the information of the successive largest lineage lengths and we prove a limit theorem for this Markov chain.

Item Type:	Article
Uncontrolled Keywords:	4901 Applied Mathematics, 49 Mathematical Sciences, 4905 Statistics
Divisions:	Faculty of Science and Engineering Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	23 Sep 2024 07:37
Last Modified:	08 Dec 2024 01:31
DOI:	10.30757/alea.v21-28
Open Access URL:	https://alea.impa.br/articles/v21/21-28.pdf
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3184652