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Keywords: Brain connectome, High dimensional regression, Influential nodes, Influential edges, Network predictors, Network shrinkage prior
This article focuses on the relationship between a measure of creativity and the human brain network of subjects from a brain connectome dataset obtained using a diffusion weighted magnetic resonance imaging (DWI) procedure. We identify brain regions and interconnections between them that have a significant effect on the creativity. Brain networks are often expressed in terms of symmetric adjacency matrices, with row and column indices of the matrix representing the regions of interest (ROI), and a cell entry signifying the estimated number of fiber bundles connecting the corresponding row and column ROIs. Current statistical practices for regression analysis with the brain network as the predictor and the measure of creativity as the response typically vectorize the network predictor matrices prior to any analysis, thus failing to account for the important structural information in the network. This results in poor inferential and predictive performance. To answer the scientific questions above, this article develops a flexible Bayesian framework that avoids reshaping the network predictor matrix, draws inference on the brain ROIs and interconnections between ROIs significantly related to creativity and enables accurate prediction of creativity from a brain network. A novel class of network shrinkage priors for the coefficient corresponding to the network predictor is proposed to achieve these inferential goals simultaneously. The principled Bayesian framework allows precise characterization of the uncertainty in detecting an ROI as influential for creativity, as well the quantification of uncertainty in prediction of creativity from a network predictor. Empirical results in simulation studies illustrate substantial inferential and predictive gains of the proposed framework in comparison with competitors. Our framework yields new insights into the relationship of brain regions with creativity, also providing the uncertainty associated with the scientific findings.