Bayesian Spatiotemporal Modeling Using Hierarchical Spatial Priors, with Applications to Functional Magnetic Resonance Imaging (with Discussion)

We propose a spatiotemporal Bayesian variable selection model for detecting activation in functional magnetic resonance imaging (fMRI) settings. Following recent research in this area, we use binary indicator variables for classifying active voxels. We assume that the spatial dependence in the images can be accommodated by applying an areal model to parcels of voxels. The use of parcellation and a spatial hierarchical prior (instead of the popular Ising prior) results in a posterior distribution amenable to exploration with an efficient Markov chain Monte Carlo algorithm. We study the properties of our approach by applying it to simulated data and to two fMRI data sets.