Bayesian Image Regression with Soft-thresholded Conditional Autoregressive Prior

In the analysis of brain functional MRI (fMRI) data using regression models, Bayesian methods are highly valued for their flexibility and ability to quantify uncertainty. However, these methods face computational challenges in high-dimensional settings typical of brain imaging, and the often pre-specified correlation structures may not accurately capture the true spatial relationships within the brain. To address these issues, we develop a general prior specifically designed for regression models with large-scale imaging data. We introduce the Soft-Thresholded Conditional AutoRegressive (ST-CAR) prior, which reduces instability to pre-fixed correlation structures and provides inclusion probabilities to account for the uncertainty in choosing active voxels in the brain. We apply the ST-CAR prior to scalar-on-image (SonI) and image-on-scalar (IonS) regression models—both critical in brain imaging studies—and develop efficient computational algorithms using variational inference (VI) and stochastic subsampling techniques. Simulation studies demonstrate that the ST-CAR prior outperforms existing methods in identifying active brain regions with complex correlation patterns, while our VI algorithms offer superior computational performance. We further validate our approach by applying the ST-CAR to working memory fMRI data from the Adolescent Brain Cognitive Development (ABCD) study, highlighting its effectiveness in practical brain imaging applications.