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

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