Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

Abstract

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.

Online Bayesian Phylogenetic Inference: Theoretical Foundations via Sequential Monte Carlo

“…In the future we will develop efficient and practical implementations of these ideas, and a first step in this direction has already been made ( Fourment et al, 2017 ). Many challenges remain.…”

“…Careful constructions of the proposal distribution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$Q^n$\end{document} , which will build \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$(n+1)$\end{document} -taxon trees out of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$n$\end{document} -taxon trees, and the Markov transition kernel \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$P^n$\end{document} are essential to cope with this increasing complexity. This goes beyond simply satisfying the criteria guaranteeing a correct sampler ( Fourment et al, 2017 ).…”

Recent advances in computational phylodynamics

“…Recently, Dinh et al [84 ] published theoretical results on the consistency and stability of such SMC methods for online Bayesian phylogenetic inference, offering important insights for future development. Fourment et al [85] show that poor placement of new sequences within the existing phylogeny can result in poor results, and guided insertion strategies are needed to tackle this problem. Further research into this direction is needed to establish a flexible and easy-to-use online…”

Peer Review #1 of "Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics (v0.1)"

“…However the quantity of sequence data being generated every year has been growing exponentially, which, when combined with practitioner's desires to conduct inference on increasingly rich statistical models, makes MCMC algorithms difficult to apply in practice because they are too slow to compute. Sequential Monte Carlo is an alternative sampling method (Doucet et al, 2001) that has recently received some attention in the phylogenetic community (Bouchard-Côté et al, 2012;Wang et al, 2015;Fourment et al, 2017). Although it is fast and, unlike MCMC algorithms, easily parallelizable, designing efficient proposals for tree topologies and continuous parameters has proven to be difficult (Fourment et al, 2017).…”

“…Sequential Monte Carlo is an alternative sampling method (Doucet et al, 2001) that has recently received some attention in the phylogenetic community (Bouchard-Côté et al, 2012;Wang et al, 2015;Fourment et al, 2017). Although it is fast and, unlike MCMC algorithms, easily parallelizable, designing efficient proposals for tree topologies and continuous parameters has proven to be difficult (Fourment et al, 2017). Unlike some statistical models, phylogenetic models have a structure that makes approximating their posterior distribution especially difficult.…”