Bayesian variable selection for logistic regression

Abstract

Abstract A key issue when using Bayesian variable selection for logistic regression is choosing an appropriate prior distribution. This can be particularly difficult for high‐dimensional data where complete separation will naturally occur in the high‐dimensional space. We propose the use of the Normal‐Gamma prior with recommendations on calibration of the hyper‐parameters. We couple this choice with the use of joint credible sets to avoid performing a search over the high‐dimensional model space. The approach is shown to outperform other methods in high‐dimensional settings, especially with highly correlated data. The Bayesian approach allows for a natural specification of the hyper‐parameters.