Ensemble MCMC Samplers for Infinite-Dimensional Bayesian Inverse Problems

Sonia Reilly, New York University

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Bayesian inverse problems seek to compute a probability distribution for the parameters of a system given noisy observations of the system output. This so-called posterior distribution may be substantially different from the prior, and/or it might be defined in a high or infinite-dimensional space – both making it challenging to be explored with sampling methods. Ensemble samplers have been shown to perform well on highly concentrated distributions in low dimensions, but fail in higher dimensions. Meanwhile, approaches such as preconditioned Crank Nicholson sampling perform robustly in high dimensions, but fail when the prior and posterior distributions differ significantly. Recent work seeks to combine these into a sampler that can perform well in both conditions. We seek to explore the potential and limitations of this novel sampler for infinite-dimensional inversion problems governed by PDEs.

Abstract Author(s): Sonia Reilly, Georg Stadler