Bayesian Joint Modeling of Multiple Brain Functional Networks

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.