© 2007 Society of Systematic Biologists
Exploring Fast Computational Strategies for Probabilistic Phylogenetic Analysis
1 Canadian Institute for Advanced Research, Département de Biochimie, Université de Montréal C.P. 6821, Succ. Centre-ville, Montréal, Québec, H3C 3J7, Canada E-mail: nicolas.rodrigue{at}umontreal.ca
2 Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, URM 5506, CNRS-Université de Montpellier 2 Montpellier, France
Edited by Paul Lewis
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Abstract |
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In recent years, the advent of Markov chain Monte Carlo (MCMC) techniques, coupled with modern computational capabilities, has enabled the study of evolutionary models without a closed form solution of the likelihood function. However, current Bayesian MCMC applications can incur significant computational costs, as they are based on a full sampling from the posterior probability distribution of the parameters of interest. Here, we draw attention as to how MCMC techniques can be embedded within normal approximation strategies for more economical statistical computation. The overall procedure is based on an estimate of the first and second moments of the likelihood function, as well as a maximum likelihood estimate. Through examples, we review several MCMC-based methods used in the statistical literature for such estimation, applying the approaches to constructing posterior distributions under non-analytical evolutionary models relaxing the assumptions of rate homogeneity, and of independence between sites. Finally, we use the procedures for conducting Bayesian model selection, based on Laplace approximations of Bayes factors, which we find to be accurate and computationally advantageous. Altogether, the methods we expound here, as well as other related approaches from the statistical literature, should prove useful when investigating increasingly complex descriptions of molecular evolution, alleviating some of the difficulties associated with nonanalytical models.
Keywords: Bayes factors; data augmentation; expectation maximization; gradient optimization; Laplace approximation; parameter expansion; thermodynamic integration
Received October 12, 2006; Revised January 29, 2007; Accepted May 30, 2007
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