The paper introduces a spectral framework that decomposes the posterior covariance in sparse Bayesian learning for M/EEG source imaging into data‑informed and indeterminacy epistemic components, using the singular value structure of the prior‑preconditioned forward operator. It also presents an equivalent subtractive decomposition that expresses the prior covariance as the sum of posterior and data‑driven reduction terms, allowing precise accounting of uncertainty reduction through Bayesian learning. These complementary representations provide both theoretical insight and practical tools for interpretable uncertainty quantification in linear‑Gaussian Bayesian inverse solvers where the posterior covariance is available in closed form.
By Ismail Huseynov, Stefan Haufe
arXiv:2609.37762v1 Announce Type: cross
Abstract: Basis-restricted priors in Bayesian inverse problems can lose coverage when the truth has components outside the basis. We show that estimating the o...
By Rares Dimitrie Grozavescu, Mark Girolami
arXiv:2606. 07196v1 Announce Type: new Abstract: Classical sparse Type-II Bayesian methods for M/EEG brain imaging support joint estimation of source and noise hyperparameters, but rely on fixed iterative update rules.
By Marco Morik, Xiao Ruiting, Shinichi Nakajima, Stefan Haufe, Ismail Huseynov
Diffusion posterior samplers reconstruct signals by combining a pretrained diffusion prior with a measurement likelihood specified by a forward model and a noise model. Calibration and reference data...
arXiv:2610.29102v1 Announce Type: new
Abstract: Diffusion posterior samplers reconstruct signals by combining a pretrained diffusion prior with a measurement likelihood specified by a forward model a...
By Wentao Shangguan, Vivek K Goyal
arXiv:2610.07824v1 Announce Type: new
Abstract: Electrophysiological source imaging (ESI) aims to estimate cortical source activity from noninvasive electrophysiological measurements such as electroe...
By Shuntaro Suzuki, Yuiga Wada, Komei Sugiura
Electrophysiological source imaging (ESI) aims to estimate cortical source activity from noninvasive electrophysiological measurements such as electroencephalogram (EEG). However, ESI is fundamentally...
arXiv:2508. 11657v2 Announce Type: replace-cross Abstract: Objective: Sparse Bayesian learning provides an effective framework to solve high-dimensional problems in brain signal decoding.
By Yuanhao Li, Badong Chen, Wenjun Bai, Yasuharu Koike, Okito Yamashita
arXiv:2607. 05165v1 Announce Type: new Abstract: Non-invasive brain-to-speech decoding aims to restore communication to patients suffering from neurodegenerative disease, without the risks of neurosurgery.
By Benjamin Ballyk, Teyun Kwon, Miran \"Ozdogan, Oiwi Parker Jones
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
By Fabian Schneider, Tapio Helin, Leila Taghizadeh
arXiv:2607. 13682v2 Announce Type: cross Abstract: Radiative Gaussian splatting reconstructs sparse-view CT fast and accurately, and recent work attaches per-Gaussian posteriors to yield per-voxel uncertainty maps.
By Chulin Zhao, Yiran Xu, Shu Liu
The paper introduces a Bayesian framework that models BOLD dynamics as coupled Ornstein‑Uhlenbeck processes and uses Sequential Neural Posterior Estimation to produce connectivity posteriors while accounting for measurement noise. Applied to 28 healthy controls scanned at 7T, the method quantifies uncertainty from scanner noise, subject variability, and scan length, revealing that about 46 voxels per ROI and 7 minutes of 7T data suffice for 90% of asymptotic precision. It also shows that 7T achieves within‑session precision 40% faster than 3T and requires roughly 37 times less per‑subject scan time to reach population‑level convergence, offering concrete, scanner‑specific guidance for protocol optimization.
By Simon Carter, Zeming Kuang, Lilianne R. Mujica-Parodi, Helmut H. Strey