Efficient estimation of expected information gain in Bayesian experimental design with multi-index Monte Carlo

Expected information gain (EIG) is an important criterion in Ba yesian optimal experimental design. Nested Monte Carlo and M ulti-level Monte Carlo (MLMC) methods have been used to compute EIG. However, in cases where the forward output function is not analytically tractable, even MLMC can not achieve its best rate. In this paper, we use Multi-index Monte Carlo to compute the EIG, which can give \( O(\varepsilon ^{-2}) \) $O({\epsilon }^{-2})$ computation work. Both theoretical analysis and numerical results are presented.