Thresholded Multiscale Gaussian Processes with Application to Bayesian Feature Selection for Massive Neuroimaging Data

Motivated by the needs of selecting important features for massive neuroimaging data, we propose a spatially varying coefficient model (SVCMs) with sparsity and piecewise smoothness imposed on the coefficient functions. A new class of nonparametric priors is developed based on thresholded multiresolution Gaussian processes (TMGP). We show that the TMGP has a large support on a space of sparse and piecewise smooth functions, leading to posterior consistency in coefficient function estimation and feature selection. Also, we develop a method for prior specifications of thresholding parameters in TMGPs and discuss their theoretical properties. Efficient posterior computation algorithms are developed by adopting a kernel convolution approach, where a modified square exponential kernel is chosen taking the advantage that the analytical form of the eigen decomposition is available. Based on simulation studies, we demonstrate that our methods can achieve better performance in estimating the spatially varying coefficient. Also, the proposed model has been applied to an analysis of resting state functional magnetic resonance imaging (Rs-fMRI) data from the Autism Brain Imaging Data Exchange (ABIDE) study, it provides biologically meaningful results.