An integrative Bayesian approach to matrix-based analysis in neuroimaging.

Understanding the correlation structure associated with brain regions is a central goal in neuroscience, as it informs about interregional relationships and network organization. Correlation structure can be conveniently captured in a matrix that indicates the relationships among brain regions, which could involve electroencephalogram sensors, electrophysiology recordings, calcium imaging data, or functional magnetic resonance imaging (FMRI) data-We call this type of analysis matrix-based analysis, or MBA. Although different methods have been developed to summarize such matrices across subjects, including univariate general linear models (GLMs), the available modeling strategies tend to disregard the interrelationships among the regions, leading to "inefficient" statistical inference. Here, we develop a Bayesian multilevel (BML) modeling framework that simultaneously integrates the analyses of all regions, region pairs (RPs), and subjects. In this approach, the intricate relationships across regions as well as across RPs are quantitatively characterized. The adoption of the Bayesian framework allows us to achieve three goals: (a) dissolve the multiple testing issue typically associated with seeking evidence for the effect of each RP under the conventional univariate GLM; (b) make inferences on effects that would be treated as "random" under the conventional linear mixed-effects framework; and (c) estimate the effect of each brain region in a manner that indexes their relative "importance". We demonstrate the BML methodology with an FMRI dataset involving a cognitive-emotional task and compare it to the conventional GLM approach in terms of model efficiency, performance, and inferences. The associated program MBA is available as part of the AFNI suite for general use.