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      An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics

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          Abstract

          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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          Phylogeny estimation: traditional and Bayesian approaches.

          The construction of evolutionary trees is now a standard part of exploratory sequence analysis. Bayesian methods for estimating trees have recently been proposed as a faster method of incorporating the power of complex statistical models into the process. Researchers who rely on comparative analyses need to understand the theoretical and practical motivations that underlie these new techniques, and how they differ from previous methods. The ability of the new approaches to address previously intractable questions is making phylogenetic analysis an essential tool in an increasing number of areas of genetic research.
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            Choosing among Partition Models in Bayesian Phylogenetics

            Bayesian phylogenetic analyses often depend on Bayes factors (BFs) to determine the optimal way to partition the data. The marginal likelihoods used to compute BFs, in turn, are most commonly estimated using the harmonic mean (HM) method, which has been shown to be inaccurate. We describe a new more accurate method for estimating the marginal likelihood of a model and compare it with the HM method on both simulated and empirical data. The new method generalizes our previously described stepping-stone (SS) approach by making use of a reference distribution parameterized using samples from the posterior distribution. This avoids one challenging aspect of the original SS method, namely the need to sample from distributions that are close (in the Kullback–Leibler sense) to the prior. We specifically address the choice of partition models and find that using the HM method can lead to a strong preference for an overpartitioned model. In contrast to the HM method and the original SS method, we show using simulated data that the generalized SS method is strikingly more precise (repeatable BF values of the same data and partition model) and yields BF values that are much more reasonable than those produced by the HM method. Comparisons of HM and generalized SS methods on an empirical data set demonstrate that the generalized SS method tends to choose simpler partition schemes that are more in line with expectation based on inferred patterns of molecular evolution. The generalized SS method shares with thermodynamic integration the need to sample from a series of distributions in addition to the posterior. Such dedicated path-based Markov chain Monte Carlo analyses appear to be a cost of estimating marginal likelihoods accurately.
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              Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods

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                Author and article information

                Journal
                22 June 2018
                Article
                1806.08813
                ec3fff7f-db2e-4a2c-a6b3-1c2cd8131c27

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                q-bio.PE stat.CO

                Evolutionary Biology,Mathematical modeling & Computation
                Evolutionary Biology, Mathematical modeling & Computation

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