Improving the Efficiency of Fully Bayesian Optimal Design of Experiments Using Randomised Quasi-Monte Carlo

Abstract

Optimal experimental design is an important methodology for most efficiently allocating resources in an experiment to best achieve some goal. Bayesian experimental design considers the potential impact that various choices of the controllable variables have on the posterior distribution of the unknowns. Optimal Bayesian design involves maximising an expected utility function, which is an analytically intractable integral over the prior predictive distribution. These integrals are typically estimated via standard Monte Carlo methods. In this paper, we demonstrate that the use of randomised quasi-Monte Carlo can bring significant reductions to the variance of the estimated expected utility. This variance reduction can then lead to a more efficient optimisation algorithm for maximising the expected utility.