Abstract

In the first part of this talk, I will present background material on Bayesian inverse problems, the associated challenges at the numerical level, and gradient-free sampling and optimization approaches for solving them.  In the second part, I will present recent work [1] on a novel gradient-free sampling method that is well suited for Bayesian inverse problems. The method is inspired by consensus-based methods in optimization and based on a stochastic interacting particle system. We demonstrate its potential in regimes where the target distribution is unimodal and close to Gaussian; indeed we prove that it enables to recover a Laplace approximation of the measure in certain parametric regimes and provide numerical evidence that this Laplace approximation attracts a large set of initial conditions in a number of examples.     [1] https://arxiv.org/abs/2106.02519