Bayesian Tensor Regression for Neuroimaging Data

Multidimensional array data, or tensors, arise naturally in neuroimaging and other high-dimensional applications. We propose a parsimonious Bayesian tensor-response regression framework for studying the association between brain images and vector-valued predictors. The approach extends Bayesian envelope methodology to tensor-valued responses, separating material variation associated with the predictors from immaterial variation and thereby reducing the effective dimension of the regression problem. The model accommodates dependence across the tensor dimensions through a separable covariance structure and provides full Bayesian uncertainty quantification. We develop posterior computation using a Gibbs sampling framework and establish posterior consistency under the proposed model. Simulation studies demonstrate substantial gains in estimation accuracy when the envelope dimension is smaller than the original tensor dimension. The methodology is illustrated using Human Connectome Project neuroimaging data to investigate associations between alcohol-use measures and brain imaging outcomes.