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A Simulation Approach for Change-Points on Phylogenetic Trees.

Persing, A; Jasra, A; Beskos, A; Balding, D; De Iorio, M; (2015) A Simulation Approach for Change-Points on Phylogenetic Trees. Journal of Computational Biology , 22 (1) 10.1089/cmb.2014.0218. Green open access

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Abstract

Abstract We observe n sequences at each of m sites and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown. The topology of the tree and branch lengths are the same for all sites, but the parameters of the evolutionary model can vary over sites. We assume a piecewise constant model for these parameters, with an unknown number of change-points and hence a transdimensional parameter space over which we seek to perform Bayesian inference. We propose two novel ideas to deal with the computational challenges of such inference. Firstly, we approximate the model based on the time machine principle: the top nodes of the binary tree (near the root) are replaced by an approximation of the true distribution; as more nodes are removed from the top of the tree, the cost of computing the likelihood is reduced linearly in n. The approach introduces a bias, which we investigate empirically. Secondly, we develop a particle marginal Metropolis-Hastings (PMMH) algorithm, that employs a sequential Monte Carlo (SMC) sampler and can use the first idea. Our time-machine PMMH algorithm copes well with one of the bottle-necks of standard computational algorithms: the transdimensional nature of the posterior distribution. The algorithm is implemented on simulated and real data examples, and we empirically demonstrate its potential to outperform competing methods based on approximate Bayesian computation (ABC) techniques.

Type: Article
Title: A Simulation Approach for Change-Points on Phylogenetic Trees.
Open access status: An open access version is available from UCL Discovery
DOI: 10.1089/cmb.2014.0218
Publisher version: http://dx.doi.org/10.1089/cmb.2014.0218
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 3.0 United States License. You are free to copy, distribute, transmit and adapt this work, but you must attribute this work as ‘‘Journal of Computational Biology.’’ Copyright 2014 Mary Ann Liebert, Inc. http://liebertpub.com/cmb, used under a Creative Commons Attribution License: http://creativecommons.org/ licenses/by/3.0/us/’’
Keywords: Approximate Bayesian Computation, Binary trees, Change-point models, Particle marginal Metropolis-Hastings, Sequential Monte Carlo samplers, Time machine
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences > Genetics, Evolution and Environment
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1447046
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