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On Bayesian calculations for mixture likelihoods and priors.

R E Weiss1, M Cho, M Yanuzzi

  • 1Department of Biostatistics, UCLA School of Public Health, Los Angeles, CA 90095-1772, USA. rob@rem.ph.ucla.edu

Statistics in Medicine
|July 9, 1999
PubMed
Summary

This study introduces a new method for calculating Bayes factors and model posterior probabilities by integrating out indicator variables before Markov chain Monte Carlo (MCMC) computations, improving accuracy over traditional methods.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • Traditional methods for model selection in Bayesian inference involve including indicator variables within Markov chain Monte Carlo (MCMC) computations.
  • This can lead to computational challenges and potential inaccuracies in estimating model probabilities.

Purpose of the Study:

  • To develop and present a novel methodology for calculating Bayes factors and posterior model probabilities.
  • To improve the accuracy and efficiency of Bayesian model selection by integrating out indicator variables prior to MCMC.

Main Methods:

  • The proposed methodology integrates indicator variables out of the posterior distribution before performing Markov chain Monte Carlo (MCMC) calculations.
  • This approach is demonstrated using the model selection prior proposed by George and McCulloch.

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  • Applications include logistic regression and mixture models within hierarchical random effects models.

    • Main Results:

    • The novel methodology yields substantially greater accuracy compared to the standard approach that includes indicator functions in MCMC.
    • Demonstrated improved precision in calculating Bayes factors and posterior model probabilities.

    Conclusions:

    • Integrating indicator variables out of the posterior before MCMC offers a more accurate approach to Bayesian model selection.
    • The presented methodology provides a valuable advancement for statistical modeling and analysis in various applications.