Computing Bayes factors using thermodynamic integration

Systematic Biology
Nicolas Lartillot, Hervé Philippe

Abstract

In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean estimation procedure. In the present article, we propose to employ another method, based on an analogy with statistical physics, called thermodynamic integration. We describe the method, propose an implementation, and show on two analytical examples that this numerical method yields reliable estimates. In contrast, the harmonic mean estimator leads to a strong overestimation of the marginal likelihood, which is all the more pronounced as the model is higher dimensional. As a result, the harmonic mean estimator systematically favors more parameter-rich models, an artefact that might explain some recent puzzling observations, based on harmonic mean estimates, suggesting that Bayes factors tend to overscore complex models. Finally, we apply our method to the comparison of several alternative models of amino-acid replacement. We confirm our previous observations, indicating that modeling pattern heterogeneity across sites tends to yield better mod...Continue Reading

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Citations

Feb 24, 2010·Proceedings of the National Academy of Sciences of the United States of America·Nicolas RodrigueNicolas Lartillot
Jan 24, 2007·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Nicolas Lartillot
Mar 15, 2012·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Serena Arima, Luca Tardella
Dec 7, 2007·Bioinformatics·Vladislav Vyshemirsky, Mark A Girolami
Aug 23, 2008·Bioinformatics·Le Si QuangNicolas Lartillot
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Mar 6, 2010·Molecular Biology and Evolution·Philippe LemeyMarc A Suchard
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