Uncertainty calibration in Bayesian M/EEG source imaging

Abstract:M/EEG source imaging requires accurate localization and reliable uncertainty estimates, yet posterior credible regions are rarely assessed for empirical calibration. We present a simulation-based framework for uncertainty quantification and calibration of empirical Bayesian inverse methods with closed-form conditional Gaussian posterior summaries. We compare Bayesian minimum norm (BMN) with sLORETA depth weighting and sparse Bayesian learning (SBL) with sparse basis field expansions (S-FLEX). S-FLEX allows retained coefficients to contribute nonzero marginal posterior variance at locations where voxel-wise SBL yields degenerate variances. For BMN, we derive joint source- and noise-variance updates through evidence maximization. We test whether adaptive noise learning yields near-calibrated uncertainties. Both methods retain residual miscalibration, motivating post-hoc isotonic recalibration of credible-region levels using empirical coverage. Simulations assess fixed- and free-orientation models across signal-to-noise ratios (SNR), source sparsity levels, and subject-specific head models, using oracle, baseline-estimated, and adaptively learned noise. Before recalibration, SBL+S-FLEX yields lower Wasserstein localization error, smaller posterior uncertainty, and coverage closer to nominal credibility than BMN+sLORETA. Isotonic recalibration improves both methods, with larger gains for conservative BMN+sLORETA posteriors; transfer across mismatched SNR, sparsity, and head models remains condition dependent. Noise specifications yield broadly consistent reconstruction and uncertainty trends within each estimator. In real auditory MEG data, SBL+S-FLEX provides more focal localization and tighter uncertainties than BMN+sLORETA, suggesting greater statistical power for identifying bilateral auditory sources. Submission history Access Paper: View PDF HTML (experimental) TeX Source Additional Features Audio Summary Current browse context: References & Citations Google Scholar Semantic Scholar Bookmark Institution arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.