  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.
