  Posterior sampling for high-dimensional Bayesian inverse problems is a common
challenge in real-world applications. Randomized Maximum Likelihood (RML) is an
optimization based methodology that gives samples from an approximation to the
posterior distribution. We develop a high-dimensional Bayesian Optimization
(BO) approach based on Gaussian Process (GP) surrogate models to solve the RML
problem. We demonstrate the benefits of our approach in comparison to
alternative optimization methods on a variety of synthetic and real-world
Bayesian inverse problems, including medical and magnetohydrodynamics
applications.
