Bayesian modelling has attracted great interest in cognitive science and offered a flexible and interpretable way to study cognitive processes using functional magnetic resonance imaging data. In this chapter, a spatial Bayesian hierarchical model is applied to an event-related fMRI study of cognitive control using the Simon test. We consider a sparse spatial generalized linear mixed-effects model to capture the spatial dependence among activated voxels and temporal parameters and to benefit computationally by reducing dimensionality. We demonstrate that the proposed model has the capability of identification of the brain areas related to cognitive tasks. Moreover, the reduction in the false positive rate is observed in the simulation study, and the relevant brain regions involved in processing cognitive control are clearly detected in a real-life fMRI example
