Detecting shared neural activity from functional magnetic resonance imaging (fMRI) across individuals exposed to the same stimulus can reveal synchronous brain responses, functional roles of regions, and potential clinical biomarkers. Intersubject correlation (ISC) is the main method for identifying voxelwise shared responses and per-subject variability, but it relies on heavy data summarization and thousands of regional tests, leading to poor uncertainty quantification and multiple testing issues. ISC also does not directly estimate a shared neural response (SNR) function. We propose a model-based alternative applicable to both task-based and naturalistic fMRI that simultaneously identifies spatial regions of shared activity and estimates the SNR function. The model combines sparse Gaussian process estimation of the response function with a Bayesian sparsity prior inspired by the horseshoe prior to detect voxel activation. A spatially structured extension encourages neighboring voxels to exhibit similar activation patterns. We examine the model's properties, evaluate performance via simulations, and analyze two real-world fMRI datasets, including one task-based and one naturalistic dataset. The Bayesian framework provides principled uncertainty quantification for the shared response function and shows improved activation detection and response estimation compared to standard approaches. Model fits demonstrate comparable or superior performance relative to ISC, while the framework opens avenues for clinical applications.
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