  Brain activation and connectivity analyses in task-based functional magnetic
resonance imaging (fMRI) experiments with multiple subjects are currently at
the forefront of data-driven neuroscience. In such experiments, interest often
lies in understanding activation of brain voxels due to external stimuli and
strong association or connectivity between the measurements on a set of
pre-specified group of brain voxels, also known as regions of interest (ROI).
This article proposes a joint Bayesian additive mixed modeling framework that
simultaneously assesses brain activation and connectivity patterns from
multiple subjects. In particular, fMRI measurements from each individual
obtained in the form of a multi-dimensional array/tensor at each time are
regressed on functions of the stimuli. We impose a low-rank PARAFAC
decomposition on the tensor regression coefficients corresponding to the
stimuli to achieve parsimony. Multiway stick breaking shrinkage priors are
employed to infer activation patterns and associated uncertainties in each
voxel. Further, the model introduces region specific random effects which are
jointly modeled with a Bayesian Gaussian graphical prior to account for the
connectivity among pairs of ROIs. Empirical investigations under various
simulation studies demonstrate the effectiveness of the method as a tool to
simultaneously assess brain activation and connectivity. The method is then
applied to a multi-subject fMRI dataset from a balloon-analog risk-taking
experiment in order to make inference about how the brain processes risk.
