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In calculating expected information gain in optimal Bayesian experimentaldesign, the computation of the inner loop in the classical double-loop MonteCarlo requires a large number of samples and suffers from underflow if thenumber of samples is small. These drawbacks can be avoided by using animportance sampling approach. We present a computationally efficient method foroptimal Bayesian experimental design that introduces importance sampling basedon the Laplace method to the inner loop. We derive the optimal values for themethod parameters in which the average computational cost is minimizedaccording to the desired error tolerance. We use three numerical examples todemonstrate the computational efficiency of our method compared with theclassical double-loop Monte Carlo, and a more recent single-loop Monte Carlomethod that uses the Laplace method as an approximation of the return value ofthe inner loop. The first example is a scalar problem that is linear in theuncertain parameter. The second example is a nonlinear scalar problem. Thethird example deals with the optimal sensor placement for an electricalimpedance tomography experiment to recover the fiber orientation in laminatecomposites.

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain