Ensemble sampler for infinite-dimensional inverse problems

TL;DR

This paper presents a novel gradient-free MCMC sampler tailored for infinite-dimensional inverse problems, leveraging an affine invariant ensemble approach that adapts to the target distribution's covariance without requiring gradients.

Contribution

The authors extend the affine invariant ensemble sampler to infinite-dimensional spaces, creating a simple, efficient, and broadly applicable MCMC method for inverse problems.

Findings

Efficient sampling in infinite-dimensional spaces without gradients.

Broad applicability to various inverse problems.

No need for posterior covariance estimates.

Abstract

We introduce a new Markov chain Monte Carlo (MCMC) sampler for infinite-dimensional inverse problems. Our new sampler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensemble sampler for the first time to infinite-dimensional function spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our new ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable.