Lagged couplings diagnose Markov chain Monte Carlo phylogenetic inference

TL;DR

This paper introduces lagged coupling methods for Markov chain Monte Carlo algorithms to diagnose convergence and mixing in complex phylogenetic inference models, enabling more reliable Bayesian analysis of evolutionary trees.

Contribution

It develops a contractive coupling approach for MCMC in phylogenetics, allowing joint convergence diagnostics across all model components and unbiased estimator construction.

Findings

Effective convergence diagnosis for phylogenetic MCMC with up to 200 leaves.

Coupled chains provide reliable assessments of mixing and convergence.

Samples from coupled chains enable unbiased estimation in complex models.

Abstract

Phylogenetic inference is an intractable statistical problem on a complex 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 or assess their performance. Existing approaches are unable to diagnose mixing or convergence of Markov schemes jointly across all components of a phylogenetic model. Lagged couplings of Markov chain Monte Carlo algorithms have recently been developed on simpler spaces to diagnose convergence and construct unbiased estimators. We describe a contractive coupling of Markov chains targeting a posterior distribution over a space of phylogenetic trees with branch lengths, scalar parameters and latent variables. We use these couplings to assess mixing and convergence of Markov chains jointly across all components of the phylogenetic model on trees with up to 200 leaves. Samples from our coupled chains may also be used to construct unbiased estimators.