An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics
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The estimation of the probability of the data under a given evolutionary model has been an important computational challenge in Bayesian phylogenetic inference. In addition, inference for nonclock trees using sequential Monte Carlo (SMC) methods has remained underexploited. In this paper, we propose an annealed SMC algorithm with the adaptive determination of annealing parameters based on the relative conditional effective sample size for Bayesian phylogenetics. The proposed annealed SMC algorithm provides an unbiased estimator for the probability of the data. This unbiasedness property can be used for the purpose of testing the correctness of posterior simulation software. We evaluate the performance of phylogenetic annealed SMC by reviewing and comparing with other normalization constant estimation methods. Unlike the previous SMC methods in phylogenetics, the annealed SMC has the same state space for all the intermediate distributions, which allows standard Markov chain Monte Carlo (MCMC) tree moves to be utilized as the basis for SMC proposal distributions. Consequently, the annealed SMC should be relatively easy to incorporate into existing phylogenetic software packages based on MCMC algorithms. We illustrate our method using simulation studies and real data analysis.
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