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Bayesian nonparametric analysis of Kingman’s coalescent
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Favaro, Stefano, Feng, Shui and Jenkins, Paul (2019) Bayesian nonparametric analysis of Kingman’s coalescent. Annales de l’Institut Henri Poincaré - Probabilites et Statistiques, 55 (2). pp. 1087-1115. doi:10.1214/18-AIHP910 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1214/18-AIHP910
Abstract
Kingman’s coalescent is one of the most popular models in population genetics. It describes the genealogy of a population whose genetic composition evolves in time according to the Wright-Fisher model, or suitable approximations of it belonging to the broad class of Fleming-Viot processes. Ancestral inference under Kingman’s coalescent has had much attention in the literature, both in practical data analysis, and from a theoretical and methodological point of view. Given a sample of individuals taken from the population at time t >0, most contributions have aimed at making frequentist or Bayesian parametric inference on quantities related to the genealogy of the sample. In this paper we propose a Bayesian non-parametric predictive approach to ancestral inference. That is, under the prior assumption that the composition of the population evolves in time according to a neutral Fleming-Viot process, and given the information contained in an initial sample of m individuals taken from the population at time t >0, we estimate quantities related to the genealogy of an additional unobservable sample of size m′≥1. As a by-product of our analysis we introduce a class of Bayesian nonparametric estimators (predictors) which can be thought of as Good-Turing type estimators for ancestral inference. The proposed approach is illustrated through an application to genetic data.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QH Natural history > QH426 Genetics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Genes -- Mathematical models, Genetics | ||||||||||||
Journal or Publication Title: | Annales de l’Institut Henri Poincaré - Probabilites et Statistiques | ||||||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||||||
ISSN: | 0246-0203 | ||||||||||||
Official Date: | 14 May 2019 | ||||||||||||
Dates: |
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Volume: | 55 | ||||||||||||
Number: | 2 | ||||||||||||
Page Range: | pp. 1087-1115 | ||||||||||||
DOI: | 10.1214/18-AIHP910 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 18 April 2018 | ||||||||||||
Date of first compliant Open Access: | 15 February 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
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