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We develop a Bayesian approach for modeling brain activation and connectivity from functional magnetic resonance image (fMRI) data. Our approach simultaneously estimates local hemodynamic response functions (HRFs) and activation parameters, as well as global effective and functional connectivity parameters. Existing methods assume identical HRFs across brain regions, which may lead to erroneous conclusions in inferring activation and connectivity patterns. Our approach addresses this limitation by estimating region-specific HRFs. Additionally, it enables neuroscientists to compare effective connectivity networks for different experimental conditions. Furthermore, the use of spike and slab priors on the connectivity parameters allows us to directly select significant effective connectivities in a given network.

We include a simulation study that demonstrates that, compared to the standard generalized linear model (GLM) approach, our model generally has higher power and lower type I error and bias than the GLM approach, and it also has the ability to capture condition-specific connectivities. We applied our approach to a dataset from a stroke study and found different effective connectivity patterns for task and rest conditions in certain brain regions of interest (ROIs).

This chapter reviews graphical modeling techniques for estimating large covariance matrices and their inverse. The chapter provides a selective survey of different models and estimators proposed by the graphical modeling literature and offers some practical examples where these methods could be applied in the area of health economics.