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Related Experiment Videos

Penalized loss functions for Bayesian model comparison.

Martyn Plummer1

  • 1International Agency for Research on Cancer, 150 Cours Albert Thomas, 69372 Lyon Cedex 08, France. plummer@iarc.fr

Biostatistics (Oxford, England)
|January 23, 2008
PubMed
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The deviance information criterion (DIC) approximates Bayesian model comparison but is unreliable for complex models like those in disease mapping. A new loss function offers a more robust alternative for mixture models.

Area of Science:

  • Statistics
  • Bayesian inference
  • Computational statistics

Background:

  • The Deviance Information Criterion (DIC) is a popular metric for Bayesian model comparison.
  • DIC lacks a rigorous theoretical foundation and relies on approximations.
  • Its validity is questionable when the number of parameters approaches the number of observations, common in fields like disease mapping.

Purpose of the Study:

  • To critically evaluate the theoretical underpinnings of the Deviance Information Criterion (DIC).
  • To investigate the limitations of DIC in complex models, such as those used in disease mapping.
  • To propose and apply an alternative deviance-based loss function suitable for mixture models.

Main Methods:

  • The study analyzes DIC as an approximation to a penalized loss function derived from cross-validation.

Related Experiment Videos

  • It examines the conditions under which this approximation holds, focusing on the ratio of effective parameters to observations.
  • A novel deviance-based loss function is derived and applied to mixture models.

    • Main Results:

    • DIC is shown to be a valid approximation only when the effective number of parameters is substantially smaller than the number of observations.
    • In disease mapping, where this condition often fails, DIC tends to under-penalize complex models.
    • The newly proposed loss function is successfully applied to mixture models, demonstrating its utility.

    Conclusions:

    • The theoretical limitations of DIC necessitate caution in its application, particularly for complex models.
    • Disease mapping applications may require alternative model comparison criteria due to DIC's shortcomings.
    • Deviance-based loss functions offer a promising and theoretically sound approach for Bayesian model comparison, especially for mixture models.