These lecture notes highlight the mathematical and computational structure relating to the
formulation of, and development of algorithms for, the Bayesian approach to inverse …

Questions of 'how best to acquire data'are essential to modelling and prediction in the
natural and social sciences, engineering applications, and beyond. Optimal experimental …

ABSTRACT A key challenge for modern Bayesian statistics is how to perform scalable
inference of posterior distributions. To address this challenge, variational Bayes (VB) …

Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture
notes volumes and research monographs plays a prominent part. The Zurich Lectures in …

Since their initial introduction, score-based diffusion models (SDMs) have been successfully
applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due …

This paper studies the learning of linear operators between infinite-dimensional Hilbert
spaces. The training data comprises pairs of random input vectors in a Hilbert space and …

Regularization and Bayesian methods for system identification have been repopularized in
the recent years, and proved to be competitive wrt classical parametric approaches. In this …

The basic idea of importance sampling is to use independent samples from a proposal
measure in order to approximate expectations with respect to a target measure. It is key to …

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting.
We consider a scale of priors of varying regularity and choose the regularity by an empirical …

We consider the inverse problem of estimating an unknown function u from noisy
measurements y of a known, possibly nonlinear, map $\mathcal {G} $ applied to u. We adopt …