Ensemble sampler for infinite-dimensional inverse problems

Jeremie Coullon, Robert Jacobs Webber

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

TL;DR: We develop an ensemble MCMC sampler for infinite-dimensional Bayesian inverse problems that doesn't require gradient or covariance information.

Abstract: We introduce a new Markov chain Monte Carlo sampler for infinite-dimensional Bayesian inverse problems. The new sampler is based on the affine invariant ensemble sampler, which we extend for the first time to function spaces. The new sampler is more efficient than preconditioned Crank-Nicolson, yet it requires no gradient information or posterior covariance information, making the sampler broadly applicable.