Open Access
August 2018 Bayesian non-parametric inference for $\Lambda$-coalescents: Posterior consistency and a parametric method
Jere Koskela, Paul A. Jenkins, Dario Spanò
Bernoulli 24(3): 2122-2153 (August 2018). DOI: 10.3150/16-BEJ923


We investigate Bayesian non-parametric inference of the $\Lambda$-measure of $\Lambda$-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 $n\in \mathbb{N}$ is constant across $\Lambda$-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.


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Jere Koskela. Paul A. Jenkins. Dario Spanò. "Bayesian non-parametric inference for $\Lambda$-coalescents: Posterior consistency and a parametric method." Bernoulli 24 (3) 2122 - 2153, August 2018.


Received: 1 July 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839262
MathSciNet: MR3757525
Digital Object Identifier: 10.3150/16-BEJ923

Keywords: Dirichlet mixture model prior , Lambda-coalescent , non-parametric inference , posterior consistency , pseudo-marginal MCMC

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
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