Recently, there has been increased interest in fusing multimodal imaging to better understand brain organization. Specifically, accounting for knowledge of anatomical pathways connecting brain regions should lead to desirable outcomes such as increased accuracy in functional brain network estimates and greater reproducibility of topological features across scanning sessions. Despite the clear merits, major challenges persist in integrative analyses including an incomplete understanding of the structure-function relationship and inaccuracies in mapping anatomical structures due to deficiencies in existing imaging technology. Clearly advanced network modeling tools are needed to appropriately incorporate anatomical structure in constructing brain functional networks. We propose a hierarchical Bayesian Gaussian graphical modeling approach that estimates the functional networks via sparse precision matrices whose degree of edge-specific shrinkage is informed by anatomical structure and an independent baseline component. The approach flexibly identifies functional connections supported by structural connectivity knowledge. This enables robust brain network estimation even in the presence of mis-specified anatomical knowledge, while accommodating heterogeneity in the structure-function relationship. We implement the approach via an efficient optimization algorithm yielding maximum a posteriori estimates. Extensive numerical studies reveal the clear advantages of our approach over competing methods in accurately estimating brain functional connectivity, even when the anatomical knowledge is mis-specified. An application of the approach to the Philadelphia Neurodevelopmental Cohort (PNC) study reveals gender based connectivity differences across multiple age groups, and higher reproducibility in the estimation of network metrics compared to alternative methods.
