Bayesian Tensor Factorized Vector Autoregressive Models for Inferring Granger Causality Patterns from High-Dimensional Multi-subject Panel Neuroimaging Data

Understanding the dynamics of functional brain connectivity patterns using noninvasive neuroimaging techniques is an important focus in human neuroscience. Vector autoregressive (VAR) processes and Granger causality analysis (GCA) have been extensively used for this purpose. While high-resolution multi-subject neuroimaging data are routinely collected now-a-days, the statistics literature on VAR models has remained heavily focused on small-to-moderate dimensional problems and single-subject data. Motivated by these issues, we develop a novel Bayesian random effects panel VAR model for multi-subject high-dimensional neuroimaging data. We begin with a single-subject model that structures the VAR coefficients as a three-way tensor, then reduces the dimensions by applying a Tucker tensor decomposition. A novel sparsity-inducing shrinkage prior allows data-adaptive rank and lag selection. We then extend the approach to a novel random effects model for multi-subject data that carefully avoids the dimensions getting exploded with the number of subjects but also flexibly accommodates subject-specific heterogeneity. We design a Markov chain Monte Carlo algorithm for posterior computation. Finally, GCA with posterior false discovery control is performed on the posterior samples. The method shows excellent empirical performance in simulation experiments. Applied to our motivating functional magnetic resonance imaging study, the approach allows the directional connectivity of human brain networks to be studied in fine detail, revealing meaningful but previously unsubstantiated cortical connectivity patterns.