Lagged couplings diagnose Markov chain Monte Carlo phylogenetic inference

Phylogenetic inference is an intractable statistical problem on a complex sample space. Markov chain Monte Carlo methods are the primary tool for Bayesian phylogenetic inference, but it is challenging to construct efficient schemes to explore the associated posterior distribution and to then assess their convergence. Building on recent work developing couplings of Monte Carlo algorithms, we describe a procedure to couple Markov Chains targeting a posterior distribution over a space of phylogenetic trees with ages, scalar parameters and latent variables. We demonstrate how to use these couplings to check convergence and mixing time of the chains.