Assessing the Convergence of Markov Chain Monte Carlo Methods for Bayesian Inference of Phylogenetic Trees

Assessing the Convergence of Markov Chain Monte Carlo Methods for Bayesian Inference of Phylogenetic Trees In biology, it is commonly of interest to investigate the ancestral pattern that gave rise to a currently existing group of individuals, such as genes or species. This ancestral pattern is frequently represented pictorially by a phylogenetic tree. Due to the growing popularity of Bayesian statistical methodology, Markov Chain Monte Carlo (MCMC) methods for Bayesian inference of phylogenetic trees have come to the forefront of phylogenetic inference. A common question is that of how long the chain must run before it can provide an approximate sample from the stationary distribution. We answer this question for a Markov chain on phylogenetic tree shapes, and provide insight into how to answer this question for a MCMC algorithm which is designed to obtain samples from the posterior distribution of the branch lengths given the tree shape and a set of DNA sequence data.