Diagnosing Markov chain Monte Carlo for phylogenetics
Luiz Max Carvalho · Proceeding Series of the Brazilian Society of Computational and Applied Mathematics · 2025
With the advent of Bayesian phylogenetics, Markov chain Monte Carlo (MCMC) methods became the de facto standard for sampling from distributions on the space of phylogenetic trees, or treespace. Treespace is vast and does not admit a canonical representation, posing difficulties to the development of not only efficient MCMC schemes but also sensitive diagnostics. In this talk I will detail recent work on the development of validation and diagnostic tools for assessing the output of phylogenetic MCMC. The talk will cover theoretical/combinatorial results on the lumpability of tree-valued processes as well as empirical/methodological work on simulation-based validation of MCMC samplers.