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Bayesian non-parametric inference for Λ-coalescents : posterior consistency and a parametric method
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Koskela, Jere, Jenkins, Paul and Spanò, Dario (2018) Bayesian non-parametric inference for Λ-coalescents : posterior consistency and a parametric method. Bernoulli, 24 (3). pp. 2122-2153. doi:10.3150/16-BEJ923 ISSN 1350-7265.
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Official URL: http://doi.org/10.3150/16-BEJ923
Abstract
We investigate Bayesian non-parametric inference of the Λ-measure of Λ-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for posterior consistency when observations form a time series, and prove that any non-trivial prior is inconsistent when all observations are contemporaneous. We then show that the likelihood given a data set of size n∈N is constant across Λ-measures whose leading n−2 moments agree, and focus on inferring truncated sequences of moments. We provide a large class of functionals which can be extremised using finite computation given a credible region of posterior truncated moment sequences, and a pseudo-marginal Metropolis–Hastings algorithm for sampling the posterior. Finally, we compare the efficiency of the exact and noisy pseudo-marginal algorithms with and without delayed acceptance acceleration using a simulation study.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QH Natural history |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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Library of Congress Subject Headings (LCSH): | Probability measures, Population genetics -- Mathematical models | |||||||||
Journal or Publication Title: | Bernoulli | |||||||||
Publisher: | Int Statistical Institute | |||||||||
ISSN: | 1350-7265 | |||||||||
Official Date: | 2 February 2018 | |||||||||
Dates: |
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Volume: | 24 | |||||||||
Number: | 3 | |||||||||
Page Range: | pp. 2122-2153 | |||||||||
DOI: | 10.3150/16-BEJ923 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 24 March 2017 | |||||||||
Date of first compliant Open Access: | 23 April 2018 | |||||||||
RIOXX Funder/Project Grant: |
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