Spatial Adaptive Selection using Binary Conditional Autoregressive Model with Application to Brain-Computer Interface.

In medical imaging studies, scalar-on-image regression presents significant challenges due to limited sample sizes and the high-dimensionality of datasets. Additionally, imaging predictors often exhibit spatially heterogeneous activation patterns and complex nonlinear associations with the response variable. To address these issues, we propose a novel Bayesian scalar-on-image regression model with the Spatial Adaptive Selection using Binary Conditional Autoregressive Model (SAS-BCAR) prior. The proposed approach leverages a binary conditional autoregressive model to capture spatial dependencies among feature selection indicators, effectively identifying spatially structured sparsity patterns within image data, while addressing nonlinear relationships between image predictors and the response variable. Furthermore, our SAS-BCAR incorporates an adaptive feature selection mechanism that adjusts to varying spatial dependencies across different image regions, ensuring a more precise and robust feature selection process. Through extensive numerical simulations on benchmark computer vision datasets and analysis of electroencephalography data in brain-computer interface applications, we demonstrate that the SAS-BCAR model achieves superior predictive performance compared to state-of-the-art alternatives, particularly in scenarios with limited training data. Supplementary materials including computer code, R packages, datasets, and additional figures are available online.