Mean-field Variational Bayes for Sparse Probit Regression

This repository is associated with the article Fasano and Rebaudo (2026+) Mean-field Variational Bayes for Sparse Probit Regression. The paper's main contribution is summarized below.

We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. [...] we develop a mean-field variational Bayes approximation in which all variational factors admit closed-form updates, and the evidence lower bound is available in closed form.

The repository contains the following R files:

• functions.R contains the needed functions to implement the algorithm, run the simulation studies and replicate the application analyses;
• parallelSimulations.R contains the code to replicate the simulation studies (specifying the values of n and p) and stores the results (Section 4 of the Manuscript);
• summarize_results.R contains the code to produce the plots of the results from the output of parallelSimulations.R (Section 4 of the Manuscript).
• VoiceApplication.R contains the code to reproduce the results of the LSVT Voice Rehabilitation application (Section 5.1 of the Manuscript).
• AlzheimerApplication.R contains the code to reproduce the results of the Alzheimer application (Section 5.2 of the Manuscript).
• VoiceSensitivityAnalysis.R contains the code to reproduce the sensitivity analysis to the specification of ν₀² in the LSVT Voice Rehabilitation application (Section S4.2 of the Supplementary Material).
• AlzheimerSensitivityAnalysis.R contains the code to reproduce the sensitivity analysis to the specification of ν₀² in the Alzheimer application (Section S4.2 of the Supplementary Material).