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Phylogenetic inference is an intractable statistical problem on a complexspace. Markov chain Monte Carlo methods are the primary tool for Bayesianphylogenetic inference but it is challenging to construct efficient schemes toexplore the associated posterior distribution or assess their performance.Existing approaches are unable to diagnose mixing or convergence of Markovschemes jointly across all components of a phylogenetic model. Lagged couplingsof Markov chain Monte Carlo algorithms have recently been developed on simplerspaces to diagnose convergence and construct unbiased estimators. We describe acontractive coupling of Markov chains targeting a posterior distribution over aspace of phylogenetic trees with branch lengths, scalar parameters and latentvariables. We use these couplings to assess mixing and convergence of Markovchains jointly across all components of the phylogenetic model on trees with upto 200 leaves. Samples from our coupled chains may also be used to constructunbiased estimators.

Lagged couplings diagnose Markov chain Monte Carlo phylogenetic inference