Gaussian Process Based Expected Information Gain Computation for Bayesian Optimal Design

Optimal experimental design (OED) is of great significance in efficient Bayesian inversion. A popular choice of OED methods is based on maximizing the expected information gain (EIG), where expensive likelihood functions are typically involved. To reduce the computational cost, in this work, a novel double-loop Bayesian Monte Carlo (DLBMC) method is developed to efficiently compute the EIG, and a Bayesian optimization (BO) strategy is proposed to obtain its maximizer only using a small number of samples. For Bayesian Monte Carlo posed on uniform and normal distributions, our analysis provides explicit expressions for the mean estimates and the bounds of their variances. The accuracy and the efficiency of our DLBMC and BO based optimal design are validated and demonstrated with numerical experiments.