Prior Knowledge Guided Ultra-high Dimensional Variable Screening with Application to Neuroimaging Data.

Abstract

Variable screening is a powerful and efficient tool for dimension reduction under ultrahigh dimensional settings. However, most existing methods overlook useful prior knowledge in specific applications. In this work, from a Bayesian modeling perspective, we develop a unified variable screening procedure for the linear regression model. We discuss different constructions of posterior mean screening (PMS) statistics to incorporate different types of prior knowledge according to specific applications. With non-informative prior specifications, PMS is equivalent to high-dimensional ordinary least-square projections (HOLP). We establish the screening consistency property for PMS with different types of prior knowledge. We show that PMS is robust to prior misspecifications; and when the prior knowledge provides correct information on summarizing the true parameter settings, PMS can substantially improve the selection accuracy compared to HOLP and other existing methods. We illustrate our method with extensive simulation studies and an analysis of neuroimaging data.