Koskela, Jere; Jenkins, Paul A.; Spanò, Dario Bayesian non-parametric inference for \(\Lambda\)-coalescents: posterior consistency and a parametric method. (English) Zbl 1419.62063 Bernoulli 24, No. 3, 2122-2153 (2018). Summary: 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. Cited in 1 Document MSC: 62G05 Nonparametric estimation 60G57 Random measures 62F15 Bayesian inference 62G20 Asymptotic properties of nonparametric inference 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 65C05 Monte Carlo methods Keywords:Dirichlet mixture model prior; Lambda-coalescent; nonparametric inference; posterior consistency; pseudo-marginal MCMC PDFBibTeX XMLCite \textit{J. Koskela} et al., Bernoulli 24, No. 3, 2122--2153 (2018; Zbl 1419.62063) Full Text: DOI arXiv Euclid