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Computing Bayes factors using thermodynamic integration.

Nicolas Lartillot1, Hervé Philippe

  • 1Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier UMR 5506, CNRS-Université, de Montpellier 2, 161, rue Ada, 34392 Montpellier Cedex 5, France. nicolas.lartillot@lirmm.fr

Systematic Biology
|March 9, 2006
PubMed
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Thermodynamic integration offers a reliable method for estimating marginal likelihoods in Bayesian model comparison. This approach avoids the overestimation issues seen with the harmonic mean estimator, particularly in complex phylogenetic models.

Area of Science:

  • Bayesian statistics
  • Phylogenetics
  • Statistical physics

Background:

  • Bayes factors are commonly used for model comparison in Bayesian inference.
  • Marginal likelihoods are crucial for Bayes factor computation.
  • Harmonic mean estimation is a prevalent but potentially flawed method for evaluating marginal likelihoods in phylogenetics.

Purpose of the Study:

  • To introduce and evaluate thermodynamic integration as an alternative method for estimating marginal likelihoods.
  • To compare the performance of thermodynamic integration against the harmonic mean estimator.
  • To investigate the impact of model complexity on marginal likelihood estimation.

Main Methods:

  • Thermodynamic integration, inspired by statistical physics, was proposed for marginal likelihood estimation.

Related Experiment Videos

  • The method was described and implemented.
  • Two analytical examples were used to test the reliability of the estimates.
  • Application to amino-acid replacement models in phylogenetics.

    • Main Results:

    • Thermodynamic integration provided reliable estimates of marginal likelihoods.
    • The harmonic mean estimator significantly overestimated marginal likelihoods, especially for higher-dimensional models.
    • This overestimation by the harmonic mean estimator systematically favors more complex models.
    • Analysis of amino-acid replacement models confirmed that modeling site heterogeneity improves model performance.

    Conclusions:

    • Thermodynamic integration is a robust and reliable method for estimating marginal likelihoods in Bayesian phylogenetics.
    • The harmonic mean estimator can lead to artefactual model selection, favoring overly complex models.
    • Accounting for pattern heterogeneity across sites is beneficial for developing better phylogenetic models.