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Conjugate Gibbs Sampling for Bayesian Phylogenetic Models

Nicolas Lartillot 1
1 MAB - Méthodes et Algorithmes pour la Bioinformatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We propose a new Markov Chain Monte Carlo (MCMC) sampling mechanism for Bayesian phylogenetic inference. This method, which we call conjugate Gibbs, relies on analytical conjugacy properties, and is based on an alternation between data augmentation and Gibbs sampling. The data augmentation step consists in sampling a detailed substitution history for each site, and across the whole tree, given the current value of the model parameters. Provided convenient priors are used, the parameters of the model can then be directly updated by a Gibbs sampling procedure, conditional on the current substitution history. Alternating between these two sampling steps yields a MCMC device whose equilibrium distribution is the posterior probability density of interest. We show, on real examples, that this conjugate Gibbs method leads to a significant improvement of the mixing behavior of the MCMC. In all cases, the decorrelation times of the resulting chains are smaller than those obtained by standard Metropolis Hastings procedures by at least one order of magnitude. The method is particularly well suited to heterogeneous models, i.e. assuming site-specific random variables. In particular, the conjugate Gibbs formalism allows one to propose efficient implementations of complex models, for instance assuming site-specific substitution processes, that would not be accessible to standard MCMC methods.
Keywords : MCMC Bayes Phylogenetics
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00135034
Contributor : Nicolas Lartillot <>
Submitted on : Tuesday, March 6, 2007 - 1:52:30 PM
Last modification on : Tuesday, November 10, 2020 - 9:28:11 AM

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  • HAL Id : lirmm-00135034, version 1

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Nicolas Lartillot. Conjugate Gibbs Sampling for Bayesian Phylogenetic Models. Journal of Computational Biology, Mary Ann Liebert, 2006, 13, pp.1701-1722. ⟨lirmm-00135034⟩

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