  Randomized Maximum Likelihood (RML) is an approximate posterior sampling
methodology, widely used in Bayesian inverse problems with complex forward
models, particularly in petroleum engineering applications. The procedure
involves solving a multi-objective optimization problem, which can be
challenging in high-dimensions and when there are constraints on computational
costs. We propose a new methodology for tackling the RML optimization problem
based on the high-dimensional Bayesian optimization literature. By sharing data
between the different objective functions, we are able to implement RML at a
greatly reduced computational cost. We demonstrate the benefits of our
methodology in comparison with the solutions obtained by alternative
optimization methods on a variety of synthetic and real-world problems,
including medical and fluid dynamics applications. Furthermore, we show that
the samples produced by our method cover well the high-posterior density
regions in all of the experiments.

Computation