Adaptive Gaussian Markov Random Fields with Applications in Human Brain Mapping

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.