Phylogenetic Inference via Sequential Monte Carlo

Bayesian inference provides an appealing general framework for phylogenetic analysis, able to incorporate a wide variety of modeling assumptions and to provide a coherent treatment of uncertainty. Existing computational approaches to Bayesian inference based on Markov chain Monte Carlo (MCMC) have not, however, kept pace with the scale of the data analysis problems in phylogenetics, and this has hindered the adoption of Bayesian methods. In this paper, we present an alternative to MCMC based on Sequential Monte Carlo (SMC). We develop an extension of classical SMC based on partially ordered sets and show how to apply this framework—which we refer to as PosetSMC—to phylogenetic analysis. We provide a theoretical treatment of PosetSMC and also present experimental evaluation of PosetSMC on both synthetic and real data. The empirical results demonstrate that PosetSMC is a very promising alternative to MCMC, providing up to two orders of magnitude faster convergence. We discuss other factors favorable to the adoption of PosetSMC in phylogenetics, including its ability to estimate marginal likelihoods, its ready implementability on parallel and distributed computing platforms, and the possibility of combining with MCMC in hybrid MCMC–SMC schemes. Software for PosetSMC is available at http://www.stat.ubc.ca/ bouchard/PosetSMC.