ABSTRACT
Department of Statistics, University of British Columbia, Vancouver, British Columbia, Canada
CONTENTS
8.1 Using phylogenetic SMC samplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.1.2 A general framework for understanding the output of
Monte Carlo algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.2 How phylogenetic SMC works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.2.1 The foundations: importance sampling . . . . . . . . . . . . . . . . . . 170 8.2.2 Toward SMC: sequential importance sampling (SIS) . . . 171 8.2.3 Resampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 8.2.4 Example: Yule trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 8.2.5 Inferring non-clock trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
8.3 Extensions and implementation issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 8.3.1 Efficiently computing and storing the particles . . . . . . . . . 178 8.3.2 More SMC proposals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 8.3.3 More on resampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8.3.4 Estimating the marginal likelihood . . . . . . . . . . . . . . . . . . . . . . 182 8.3.5 Combining SMC and MCMC . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Until recently, Markov chain Monte Carlo (MCMC) has been the lone, faithful workhorse of Bayesian phylogenetics. MCMC methods have turned an abstract decision theoretic framework into a practical toolbox that has been applied to most phylogenetic inferential questions.
