A Surrogate Function for One-Dimensional Phylogenetic Likelihoods

Adaptive Tree Proposals for Bayesian Phylogenetic Inference

Bayesian inference of phylogeny with MCMC plays a key role in the study of evolution. Yet, this method still suffers from a practical challenge identified more than two decades ago: designing tree topology proposals that efficiently sample tree spaces. In this article, I introduce the concept of adaptive tree proposals for unrooted topologies, that is tree proposals adapting to the posterior distribution as it is estimated. I use this concept to elaborate two adaptive variants of existing proposals and an adaptive proposal based on a novel design philosophy in which the structure of the proposal is informed by the posterior distribution of trees. I investigate the performance of these proposals by first presenting a metric that captures the performance of each proposal within a mixture of proposals. Using this metric, I compare the performance of the adaptive proposals to the performance of standard and parsimony-guided proposals on 11 empirical datasets. Using adaptive proposals led to consistent performance gains and resulted in up to 18-fold increases in mixing efficiency and 6-fold increases in convergence rate without increasing the computational cost of these analyses.

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy.