Bayesian variable selection for logistic regression

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.