Functional magnetic resonance imaging (fMRI) has become the standard technology in human brain mapping. Analyses of the massive spatio-temporal fMRI data sets often focus on parametric or nonparametric modeling of the temporal component, while spatial smoothing is based on Gaussian kernels or random fields. A weakness of Gaussian spatial smoothing is underestimation of activation peaks or blurring of high-curvature transitions between activated and non-activated brain regions. In this paper, we introduce a class of inhomogeneous Markov random fields (MRF) with spatially adaptive interaction weights in a space-varying coefficient model for fMRI data. For given weights, the random field is conditionally Gaussian, but marginally it is non-Gaussian. Fully Bayesian inference, including estimation of weights and variance parameters, is carried out through efficient MCMC simulation. An application to fMRI data from a visual stimulation experiment demonstrates the performance of our approach in comparison to Gaussian and robustified non-Gaussian Markov random field models
