Bayesian posterior distributions on phylogenetic trees remain difficult to sample despite decades of effort. The complex discrete and continuous model structure of trees means that recent statistical samplers developed for Euclidean space are not applicable to the phylogenetic case. Thus, we are left with random-walk Markov Chain Monte Carlo with uninformed tree modification proposals. These methods traverse tree space slowly because phylogenetic posteriors are concentrated on a small fraction of the very many possible trees.
In this talk, I will describe our recent work moving beyond random walk MCMC sampling of posterior distributions on phylogenetic trees. This includes (1) an online sequential Monte Carlo algorithm that can update existing posterior inferences when additional sequences arrive, (2) an extension of Hamiltonian Monte Carlo to simultaneously explore discrete and continuous aspects of tree space, and (3) "phylogenetic topographer," a strategy to systematically map out the posterior distribution and provide an approximate posterior weight.