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Computational Inference Beyond Kingman's Coalescent

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Jere Koskela ,
Paul Jenkins  and
Dario Spanò
Jere Koskela*
Affiliation:
University of Warwick
Paul Jenkins*
Affiliation:
University of Warwick
Dario Spanò*
Affiliation:
University of Warwick
*
∗ Postal address: Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK. Email address: j.j.koskela@warwick.ac.uk
∗∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
∗∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

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Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) methods have been applied successfully. Both methods can be expressed in terms of families of intractable conditional sampling distributions (CSDs), and rely on principled approximations for accurate inference. Recently, more general Λ- and Ξ-coalescents have been observed to provide better modelling fits to some genetic data sets. We derive families of approximate CSDs for finite sites Λ- and Ξ-coalescents, and use them to obtain ‘approximately optimal’ IS and PAC algorithms for Λ-coalescents, yielding substantial gains in efficiency over existing methods.

Keywords

Lambda-coalescentxi-coalescentproduct of approximate conditionalsimportance samplingconditional sampling distributionpopulation genetics

MSC classification

Primary: 60G09: Exchangeability
Secondary: 93E10: Estimation and detection 92D25: Population dynamics (general)
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 519 - 537
Copyright
© Applied Probability Trust 

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