Sequential Design of Computer Experiments for the Solution of Bayesian Inverse Problems

Abstract

We present a sequential design strategy for efficient sampling of model functions during the solution of Bayesian inverse problems. The model function is assumed to be computationally expensive and therefore is described by a random field (such as a Gaussian process emulator). The sequential design strategy is a greedy one-step look ahead method, minimizing the Bayes risk with respect to a loss function measuring the quadratic $L^2$-error in the likelihood estimate. Four numerical examples demonstrate that the proposed sampling method is more efficient than space-filling, prior-based designs.