Using an informed reversible jump for variable selection under a Bayesian framework with an application to schizophrenia data

Symptom based diagnosis are known to be limited specially concerning complex disorders such as schizophrenia and modern attempts in providing predictive risk to assist existing diagnosis tools relies on brain information such as functional Magnetic Resonance Image (fMRI).Using the fMRI, segmented into region of interest (ROI) in the brain, of healthy and people diagnosed with schizophrenia, we propose a Bayesian probit model to select discriminating ROI, achieved using a data driven reversible jump markov chain monte carlo. We also compare our methodology to a Bayesian logistic regression with a regularized horseshoe prior and Lasso in terms of selected variables and predictive performance.