An Efficient Independence Sampler for Updating Branches in Bayesian Markov chain Monte Carlo Sampling of Phylogenetic Trees

Abstract.—Sampling tree space is the most challenging aspect of Bayesian phylogenetic inference. The sheer number of alternative topologies is problematic by itself. In addition, the complex dependency between branch lengths and topology increases the difficulty of moving efficiently among topologies. Current tree proposals are fast but sample new trees using primitive transformations or re-mappings of old branch lengths. This reduces acceptance rates and presumably slows down convergence and mixing. Here, we explore branch proposals that do not rely on old branch lengths but instead are based on approximations of the conditional posterior. Using a diverse set of empirical data sets, we show that most conditional branch posteriors can be accurately approximated via a distribution. We empirically determine the relationship between the logarithmic conditional posterior density, its derivatives, and the characteristics of the branch posterior. We use thes