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June 2020 Sequential importance sampling for multiresolution Kingman–Tajima coalescent counting
Lorenzo Cappello, Julia A. Palacios
Ann. Appl. Stat. 14(2): 727-751 (June 2020). DOI: 10.1214/19-AOAS1313

Abstract

Statistical inference of evolutionary parameters from molecular sequence data relies on coalescent models to account for the shared genealogical ancestry of the samples. However, inferential algorithms do not scale to available data sets. A strategy to improve computational efficiency is to rely on simpler coalescent and mutation models, resulting in smaller hidden state spaces. An estimate of the cardinality of the state space of genealogical trees at different resolutions is essential to decide the best modeling strategy for a given dataset. To our knowledge, there is neither an exact nor approximate method to determine these cardinalities. We propose a sequential importance sampling algorithm to estimate the cardinality of the sample space of genealogical trees under different coalescent resolutions. Our sampling scheme proceeds sequentially across the set of combinatorial constraints imposed by the data which, in this work, are completely linked sequences of DNA at a nonrecombining segment. We analyze the cardinality of different genealogical tree spaces on simulations to study the settings that favor coarser resolutions. We apply our method to estimate the cardinality of genealogical tree spaces from mtDNA data from the 1000 genomes and a sample from a Melanesian population at the $\beta $-globin locus.

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Lorenzo Cappello. Julia A. Palacios. "Sequential importance sampling for multiresolution Kingman–Tajima coalescent counting." Ann. Appl. Stat. 14 (2) 727 - 751, June 2020. https://doi.org/10.1214/19-AOAS1313

Information

Received: 1 February 2019; Revised: 1 September 2019; Published: June 2020
First available in Project Euclid: 29 June 2020

zbMATH: 07239881
MathSciNet: MR4117827
Digital Object Identifier: 10.1214/19-AOAS1313

Keywords: Coalescent , enumeration , sequential importance sampling

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June 2020
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