Bayesian Joint Modeling of Multiple Brain Functional Networks.

Investigating the similarity and changes in brain networks under different mental conditions has become increasingly important in neuroscience research. A standard separate estimation strategy fails to pool information across networks and hence has reduced estimation accuracy and power to detect between-network differences. Motivated by a fMRI Stroop task experiment that involves multiple related tasks, we develop an integrative Bayesian approach for jointly modeling multiple brain networks that provides a systematic inferential framework for network comparisons. The proposed approach explicitly models shared and differential patterns via flexible Dirichlet process-based priors on edge probabilities. Conditional on edges, the connection strengths are modeled via Bayesian spike and slab prior on the precision matrix off-diagonals. Numerical simulations illustrate that the proposed approach has increased power to detect true differential edges while providing adequate control on false positives and achieves greater network estimation accuracy compared to existing methods. The Stroop task data analysis reveals greater connectivity differences between task and fixation that are concentrated in brain regions previously identified as differentially activated in Stroop task, and more nuanced connectivity differences between exertion and relaxed task. In contrast, penalized modeling approaches involving computationally burdensome permutation tests reveal negligible network differences between conditions that seem biologically implausible.