  Mediation analysis aims to separate the indirect effect through mediators
from the direct effect of the exposure on the outcome. It is challenging to
perform mediation analysis with neuroimaging data which involves high
dimensionality, complex spatial correlations, sparse activation patterns and
relatively low signal-to-noise ratio. To address these issues, we develop a new
spatially varying coefficient structural equation model for Bayesian Image
Mediation Analysis (BIMA). We define spatially varying mediation effects within
the potential outcome framework, employing the soft-thresholded Gaussian
process prior for functional parameters. We establish the posterior consistency
for spatially varying mediation effects along with selection consistency on
important regions that contribute to the mediation effects. We develop an
efficient posterior computation algorithm scalable to analysis of large-scale
imaging data. Through extensive simulations, we show that BIMA can improve the
estimation accuracy and computational efficiency for high-dimensional mediation
analysis over the existing methods. We apply BIMA to analyze the behavioral and
fMRI data in the Adolescent Brain Cognitive Development (ABCD) study with a
focus on inferring the mediation effects of the parental education level on the
children's general cognitive ability that are mediated through the working
memory brain activities.
