Using prior-data conflict to tune Bayesian regularized regression models
Date
2023-09-22
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Abstract
In high-dimensional regression models, variable selection becomes challenging from a computational and theoretical perspective. Bayesian regularized regression via shrinkage priors like the Laplace or spike-and-slab prior are effective methods for variable selection in p > n scenarios provided the shrinkage priors are configured adequately. We propose configuring shrinkage priors using checks for prior-data conflict: tests that assess whether there is disagreement in parameter information provided by the prior and data. We apply our proposed method to the Bayesian LASSO and spike-and-slab shrinkage priors and assess variable selection performance of our prior configurations against competing models through a linear and logistic high-dimensional simulation study. Additionally, we apply our method to proteomic data collected from patients admitted to the Albany Medical Center in Albany NY in April of 2020 with COVID-like respiratory issues. Simulation results suggest our proposed configurations may outperform competing models when the true regression effects are small.
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Keywords
Biostatistics, Bayesian statistics
Citation
Biziaev, T. (2023). Using prior-data conflict to tune Bayesian regularized regression models (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.