Some evidence suggests that people with autism spectrum disorder exhibit patterns of brain functional dysconnectivity relative to their typically developing peers, but specific findings have yet to be replicated. To facilitate this replication goal with data from the Autism Brain Imaging Data Exchange (ABIDE), we propose a flexible and interpretable model for participant-specific voxel-level brain functional connectivity. Our approach efficiently handles massive participant-specific whole brain voxel-level connectivity data that exceed one trillion data points. The key component of the model is to leverage the block structure induced by defined regions of interest to introduce parsimony in the high-dimensional connectivity matrix through a block covariance structure. Associations between brain functional connectivity and participant characteristics -- including eye status during the resting scan, sex, age, and their interactions -- are estimated within a Bayesian framework. A spike-and-slab prior facilitates hypothesis testing to identify voxels associated with autism diagnosis. Simulation studies are conducted to evaluate the empirical performance of the proposed model and estimation framework. In ABIDE, the method replicates key findings from the literature and suggests new associations for investigation.

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