Titre:
Consensus-based sampling
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
