Fast, fully Bayesian spatiotemporal inference for fMRI data.

We propose a spatial Bayesian variable selection method for detecting blood oxygenation level dependent activation in functional magnetic resonance imaging (fMRI) data. Typical fMRI experiments generate large datasets that exhibit complex spatial and temporal dependence. Fitting a full statistical model to such data can be so computationally burdensome that many practitioners resort to fitting oversimplified models, which can lead to lower quality inference. We develop a full statistical model that permits efficient computation. Our approach eases the computational burden in two ways. We partition the brain into 3D parcels, and fit our model to the parcels in parallel. Voxel-level activation within each parcel is modeled as regressions located on a lattice. Regressors represent the magnitude of change in blood oxygenation in response to a stimulus, while a latent indicator for each regressor represents whether the change is zero or non-zero. A sparse spatial generalized linear mixed model captures the spatial dependence among indicator variables within a parcel and for a given stimulus. The sparse SGLMM permits considerably more efficient computation than does the spatial model typically employed in fMRI. Through simulation we show that our parcellation scheme performs well in various realistic scenarios. Importantly, indicator variables on the boundary between parcels do not exhibit edge effects. We conclude by applying our methodology to data from a task-based fMRI experiment.