Bayesian non-parametric inference for Λ-coalescents: Posterior consistency and a parametric method

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...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2018-08, Vol.24 (3), p.2122-2153
Main Authors: KOSKELA, JERE, JENKINS, PAUL A., SPANÒ, DARIO
Format: Article
Language:English
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Summary: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.
ISSN:1350-7265
DOI:10.3150/16-BEJ923