Focused information criteria for model selection - a Bayesian perspective.

Area of Science:

• Statistics
• Biostatistics
• Bayesian Inference

Background:

• Traditional model selection criteria (AIC, WAIC) assess global prediction accuracy.
• These criteria may not be optimal when the focus is on specific model parameters.
• The frequentist Focused Information Criterion (FIC) addresses this by measuring focus parameter mean squared error.

Purpose of the Study:

• To introduce the Bayesian Focused Information Criterion (BFIC) as a Bayesian analog to the FIC.
• To adapt the FIC for model selection in a Bayesian context using posterior distributions.
• To apply the BFIC for selecting models that best describe BMI trajectory differences in newborns based on birth weight.

Main Methods:

• Developed the Bayesian Focused Information Criterion (BFIC) using posterior distributions.
• Estimated the mean square error of focus parameters within a Bayesian framework.
• Applied the BFIC to a longitudinal newborn growth dataset to select models for BMI trajectory analysis.

Main Results:

• The BFIC was successfully applied to a real-world dataset.
• The proposed method allowed for model selection based on specific parameter of interest (average BMI at one year).
• Demonstrated the utility of BFIC in analyzing differences in BMI trajectories across birth weight classes.

Conclusions:

• The Bayesian Focused Information Criterion provides a valuable tool for Bayesian model selection when specific parameters are of interest.
• BFIC offers a robust method for estimating parameter-specific mean squared error in Bayesian analysis.
• This approach is effective for research questions involving subgroup comparisons, such as BMI development in newborns.