Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractIn calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized for a specified error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a single-loop Monte Carlo method that uses the Laplace approximation of the return value of the inner loop. The first demonstration example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.
CitationBeck J, Dia BM, Espath LFR, Long Q, Tempone R (2018) Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain. Computer Methods in Applied Mechanics and Engineering 334: 523–553. Available: http://dx.doi.org/10.1016/j.cma.2018.01.053.
SponsorsThe research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST); KAUST CRG3 Award Ref:2281 and the KAUST CRG4 Award Ref:2584.