Particle filters contain the promise of fully nonlinear data assimilation. They have been
applied in numerous science areas, including the geosciences, but their application to high …

Stein's method compares probability distributions through the study of a class of linear
operators called Stein operators. While mainly studied in probability and used to underpin …

This open-access textbook's significant contribution is the unified derivation of data-
assimilation techniques from a common fundamental and optimal starting point, namely …

Variational inference (VI) seeks to approximate a target distribution $\pi $ by an element of a
tractable family of distributions. Of key interest in statistics and machine learning is Gaussian …

Solving inverse problems without the use of derivatives or adjoints of the forward model is
highly desirable in many applications arising in science and engineering. In this paper we …

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear
dynamical systems as it provides coordinate transformations to globally linearize the …

Statistical Optimal Transport arxiv:2407.18163v2 [math.ST] 7 Nov 2024 Page 1 Statistical
Optimal Transport Sinho Chewi Yale Jonathan Niles-Weed NYU Philippe Rigollet MIT …

Bayesian inference problems require sampling or approximating high-dimensional
probability distributions. The focus of this paper is on the recently introduced Stein …

Abstract We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises
a set of particles to approximate a target probability distribution $\pi\propto e^{-V} $ on $\R …

Training nonlinear parametrizations such as deep neural networks to numerically
approximate solutions of partial differential equations is often based on minimizing a loss …