Bayesian inference provides a robust framework for combining prior knowledge with new evidence to update beliefs about uncertain quantities. In the context of statistical inverse problems, this ...

Check back in Fall 2025. Abstract: Constitutive or material models provide a mathematical description of how solids respond to mechanical stimuli. For example, an isotropic linear elastic constitutive ...

The Bayesian approach to ill-posed operator equations in Hilbert space recently gained attraction. In this context, and when the prior distribution is Gaussian, then two operators play a significant ...

In the context of inverse problems, a mathematical model of the measurements is called the direct problem. To understand this term, let us consider a model for obstetric sonography. An ultrasonic ...

Bayesian inverse problems with Laplacian noise We are interested in Bayesian inverse problems on function spaces with non-Gaussian noise. In the case of Gaussian noise and a Gaussian prior, MAP ...

M. Liu, J. Narciso, D. Grana, E. Van De Vijver, and L. Azevedo, 2023, Frequency-domain electromagnetic induction for the prediction of electrical conductivity and magnetic susceptibility using ...

Up to now we have formulated the learning problem in terms of a function having a simple, e.g., pointwise, relation to . Nonlocalities in the relation between and was only due to the normalization ...