Bayesian Phylogenetic Inference Using a Combinatorial Sequential Monte Carlo Method

Abstract

The application of Bayesian methods to large-scale phylogenetics problems is increasingly limited by computational issues, motivating the development of methods that can complement existing Markov chain Monte Carlo (MCMC) schemes. Sequential Monte Carlo (SMC) methods are approximate inference algorithms that have become very popular for time series models. Such methods have been recently developed to address phylogenetic inference problems but currently available techniques are only applicable to a restricted class of phylogenetic tree models compared to MCMC. In this article, we propose an original combinatorial SMC (CSMC) method to approximate posterior phylogenetic tree distributions, which is applicable to a general class of models and can be easily combined with MCMC to infer evolutionary parameters. Our method only relies on the existence of a flexible partially ordered set structure and is more generally applicable to sampling problems on combinatorial spaces. We demonstrate that the proposed CSMC algorithm provides consistent estimates under weak assumptions, is computationally fast, and is additionally easily parallelizable. Supplementary materials for this article are available online.

• Bayesian inference
• Particle Markov chain Monte Carlo
• Phylogenetics
• Poset
• Sequential Monte Carlo

Additional information

Notes on contributors

Liangliang Wang

Liangliang Wang is Assistant Professor, Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (E-mail: [email protected]). Alexandre Bouchard-Côté is Assistant Professor, Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (E-mail: [email protected]). Arnaud Doucet is Professor, Department of Statistics, Oxford University, Oxford, United Kingdom (E-mail: [email protected]). The authors thank the editor, the associate editor, the reviewers, and Jens Lagergren from KTH Royal Institute of Technology for their constructive comments that helped improve the article significantly. The authors are also grateful to Westgrid for the computing support. This research was supported by grants from the Natural Science and Engineering Research Council of Canada to Liangliang Wang and Alexandre Bouchard-Côté. Arnaud Doucet’s research was partly funded by the Engineering and Physical Sciences Research Councils under grants EP/K000276/1 and EP/K009850/1.

Alexandre Bouchard-Côté

Liangliang Wang is Assistant Professor, Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (E-mail: [email protected]). Alexandre Bouchard-Côté is Assistant Professor, Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (E-mail: [email protected]). Arnaud Doucet is Professor, Department of Statistics, Oxford University, Oxford, United Kingdom (E-mail: [email protected]). The authors thank the editor, the associate editor, the reviewers, and Jens Lagergren from KTH Royal Institute of Technology for their constructive comments that helped improve the article significantly. The authors are also grateful to Westgrid for the computing support. This research was supported by grants from the Natural Science and Engineering Research Council of Canada to Liangliang Wang and Alexandre Bouchard-Côté. Arnaud Doucet’s research was partly funded by the Engineering and Physical Sciences Research Councils under grants EP/K000276/1 and EP/K009850/1.

Arnaud Doucet

Liangliang Wang is Assistant Professor, Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada (E-mail: [email protected]). Alexandre Bouchard-Côté is Assistant Professor, Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (E-mail: [email protected]). Arnaud Doucet is Professor, Department of Statistics, Oxford University, Oxford, United Kingdom (E-mail: [email protected]). The authors thank the editor, the associate editor, the reviewers, and Jens Lagergren from KTH Royal Institute of Technology for their constructive comments that helped improve the article significantly. The authors are also grateful to Westgrid for the computing support. This research was supported by grants from the Natural Science and Engineering Research Council of Canada to Liangliang Wang and Alexandre Bouchard-Côté. Arnaud Doucet’s research was partly funded by the Engineering and Physical Sciences Research Councils under grants EP/K000276/1 and EP/K009850/1.