  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.
