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Summary
This summary is machine-generated.

The Deviance Information Criterion (DIC) often overfits models, showing high sensitivity but poor correct selection rates (0-2%) in Bayesian model selection, even with large sample sizes. Marginal likelihood criteria offer better asymptotic performance, avoiding DIC's persistent mis-selection issues.

Keywords:
Deviance Information CriterionHighest Posterior Modelg-priormis-selction

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Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • Bayesian model selection commonly employs criteria like the Highest Posterior Model (HPM) and the Deviance Information Criterion (DIC).
  • The DIC is widely used due to its ease of estimation via sampling methods and availability in Bayesian software.
  • DIC's practical utility is contrasted with its theoretical performance in model selection accuracy.

Purpose of the Study:

  • To evaluate the performance of the Deviance Information Criterion (DIC) and marginal likelihood in Bayesian criterion-based model selection.
  • To investigate the sensitivity and correct selection rates of DIC across varying sample sizes.
  • To compare the asymptotic properties of DIC and marginal likelihood, particularly regarding mis-selection probabilities.

Main Methods:

  • Analysis of Bayesian criterion-based selection methods, focusing on Highest Posterior Model (HPM) and Deviance Information Criterion (DIC).
  • Theoretical analysis of asymptotic behavior and mis-selection probabilities for DIC and marginal likelihood.
  • Simulation studies and application to a biomarker selection problem in non-small cell lung cancer patient data.

Main Results:

  • DIC exhibits high sensitivity (90-100%) but very low correct selection rates (0-2%), consistent across sample sizes.
  • Both DIC and marginal likelihood asymptotically penalize under-fitted models.
  • DIC's mis-selection probability is bounded away from zero in linear models with specific priors, unlike marginal likelihood which can converge to zero.
  • DIC fails to asymptotically distinguish between data-generating, over-fitted, and even two over-fitted models.

Conclusions:

  • The Deviance Information Criterion (DIC) demonstrates significant limitations in accurate Bayesian model selection, often favoring over-fitted models.
  • Marginal likelihood criteria offer superior asymptotic properties for model selection compared to DIC.
  • Findings highlight the need for caution when using DIC, especially in complex models or when precise model selection is critical, prompting consideration of alternatives like HPM or marginal likelihood.