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estimation accuracy. In addition, the uncertainty measures provided by our method correlate with estimation errors and produce reasonable confidence intervals; these results suggest potential application of the proposed uncertainty quantification method in brain studies. Characterizing functional brain connectivity using resting functional magnetic resonance imaging (fMRI) is challenging due to the relatively small Blood-Oxygen-Level Dependent contrast and low signal-to-noise ratio. Denoising using surface-based Laplace-Beltrami (L o