SIGHR: Side information guided high-dimensional regression

Abstract

In this work, we develop a novel Bayesian regression framework that can be used to complete variable selection in high dimensional settings. Unlike existing techniques, the proposed approach can leverage side information to inform about the sparsity structure of the regression coefficients. This is accomplished by replacing the usual inclusion probability in the spike and slab prior with a binary regression model which assimilates this extra source of information. To facilitate model fitting, a computationally efficient and easy to implement Markov chain Monte Carlo posterior sampling algorithm is developed via carefully chosen priors and data augmentation steps. The finite sample performance of our methodology is assessed through numerical simulations, and we further illustrate our approach by using it to identify genetic markers associated with the nicotine metabolite ratio; a key biological marker associated with nicotine dependence and smoking cessation treatment.