  Brain function is organized in coordinated modes of spatio-temporal activity
(functional networks) exhibiting an intrinsic baseline structure with
variations under different experimental conditions. Existing approaches for
uncovering such network structures typically do not explicitly model shared and
differential patterns across networks, thus potentially reducing the detection
power. We develop an integrative modeling approach for jointly modeling
multiple brain networks across experimental conditions. The proposed Bayesian
Joint Network Learning approach develops flexible priors on the edge
probabilities involving a common intrinsic baseline structure and differential
effects specific to individual networks. Conditional on these edge
probabilities, connection strengths are modeled under a Bayesian spike and slab
prior on the off-diagonal elements of the inverse covariance matrix. The model
is fit under a posterior computation scheme based on Markov chain Monte Carlo.
Numerical simulations illustrate that the proposed joint modeling approach has
increased power to detect true differential edges while providing adequate
control on false positives and achieving greater accuracy in the estimation of
edge strengths compared to existing methods. An application of the method to
fMRI Stroop task data provides unique insights into brain network alterations
between cognitive conditions which existing graphical modeling techniques
failed to reveal.
