Using prior-data conflict to tune Bayesian regularized regression models.

Area of Science:

• Statistics
• Computational Biology
• Biostatistics

Background:

• High-dimensional regression models present computational and theoretical challenges for variable selection.
• Bayesian regularized regression with shrinkage priors (e.g., Laplace, spike-and-slab) offers effective variable selection when priors are well-configured.

Purpose of the Study:

• To propose an empirical Bayes configuration method for shrinkage priors in Bayesian regularized regression.
• To assess the performance of this method in variable selection for high-dimensional linear regression models.

Main Methods:

• Developed an empirical Bayes configuration using prior-data conflict checks.
• Applied the method to Bayesian LASSO and spike-and-slab priors.
• Evaluated performance via high-dimensional simulations and analysis of COVID-19 proteomic data.

Main Results:

• The proposed empirical Bayes configuration shows potential to outperform competing models, particularly when true regression effects are small.
• The method was successfully applied to both simulated data and real-world proteomic data.

Conclusions:

• Empirical Bayes configuration with prior-data conflict checks offers a robust approach for variable selection in Bayesian regularized regression.
• This method enhances the reliability and performance of Bayesian variable selection techniques in complex datasets.