Geometric ergodicity of a Metropolis-Hastings algorithm for Bayesian inference of phylogenetic branch lengths

This manuscript extends the work of Spade et al. (Math Biosci 268:9–21, 2015) to an examination of a fully-updating version of a Metropolis-Hastings algorithm for inference of phylogenetic branch lengths. This approach serves as an intermediary between theoretical assessment of Markov chain convergence, which in phylogenetic settings is typically difficult to do analytically, and output-based convergence diagnostics, which suffer from several of their own limitations. In this manuscript, we will also examine the performance of the convergence assessment techniques for this Markov chain and the convergence behavior of this type of Markov chain compared to the one-at-a-time updating scheme investigated in Spade et al. (Math Biosci 268:9–21, 2015). We will also vary the choices of the drift function in order to obtain a sense of how the choice of the drift function affects the estimated bound on the chain’s mixing time.