Ensemble MCMC Sampling for Infinite-Dimensional Bayesian Inverse Problems

Bayesian inverse problems use noisy measurements of the output of a system, such as the solution of a PDE, to infer a posterior probability distribution over the parameters of the system. When these parameters are functions, the probability distributions are defined over infinite-dimensional spaces. This infinite dimensionality renders most of the traditional approaches to sampling distributions ineffective. Efforts to sample from the posterior distributions are further complicated in the case when the posterior differs greatly from the prior. We propose an ensemble Markov Chain Monte Carlo sampling algorithm that is robust to the discretization dimension of the infinite-dimensional problem, and remains efficient when the posterior differs substantially from the prior.