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We address the computational efficiency in solving the A-optimal Bayesiandesign of experiments problems for which the observational map is based onpartial differential equations and, consequently, is computationally expensiveto evaluate. A-optimality is a widely used and easy-to-interpret criterion forBayesian experimental design. This criterion seeks the optimal experimentaldesign by minimizing the expected conditional variance, which is also known asthe expected posterior variance. This study presents a novel likelihood-freeapproach to the A-optimal experimental design that does not require sampling orintegrating the Bayesian posterior distribution. The expected conditionalvariance is obtained via the variance of the conditional expectation using thelaw of total variance, and we take advantage of the orthogonal projectionproperty to approximate the conditional expectation. We derive an asymptoticerror estimation for the proposed estimator of the expected conditionalvariance and show that the intractability of the posterior distribution doesnot affect the performance of our approach. We use an artificial neural network(ANN) to approximate the nonlinear conditional expectation in theimplementation of our method. We then extend our approach for dealing with thecase that the domain of experimental design parameters is continuous byintegrating the training process of the ANN into minimizing the expectedconditional variance. Through numerical experiments, we demonstrate that ourmethod greatly reduces the number of observation model evaluations comparedwith widely used importance sampling-based approaches. This reduction iscrucial, considering the high computational cost of the observational models.Code is available at https://github.com/vinh-tr-hoang/DOEviaPACE.

Scalable method for Bayesian experimental design without integrating over posterior distribution