Bayesian model evidence as a practical alternative to deviance information criterion.

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• Bayesian model evidence is the gold standard for model selection but often computationally intensive.
• Deviance Information Criterion (DIC) is a faster, widely used alternative that balances model accuracy and complexity.
• Recent advances in Markov chain Monte Carlo (MCMC) algorithms, like steppingstone sampling (SS), enable efficient Bayesian model evidence calculation.

Purpose of the Study:

• To compare the capability and speed of DIC versus Bayesian model evidence calculated using SS for model selection.
• To evaluate performance across linear regression, mixed models, and epidemiological compartmental models.

Main Methods:

• Comparison of Deviance Information Criterion (DIC) and Bayesian model evidence computed via steppingstone sampling (SS).
• Assessment of model selection accuracy (capability) and computational time (speed).
• Application to three distinct model classes: linear regression, mixed models, and compartmental models.

Main Results:

• DIC correctly selected the true model for linear regression but failed for mixed and compartmental models.
• Bayesian model evidence, calculated using SS, correctly identified the true model in all considered cases.
• DIC and Bayesian model evidence exhibited similar computational speeds, contrary to common assumptions.

Conclusions:

• Bayesian model evidence, efficiently computed with SS, is a more reliable method for model selection than DIC, especially for complex models.
• The computational cost of Bayesian model evidence is comparable to DIC, challenging the notion that DIC is significantly faster.
• Steppingstone sampling provides an efficient pathway to utilize Bayesian model evidence for robust statistical modeling.