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

Joakim Beck, Ben Mansour Dia*, Luis F.R. Espath, Quan Long, Raúl Tempone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


In 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.

Original languageEnglish (US)
Pages (from-to)523-553
Number of pages31
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jun 1 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.


  • Bayesian experimental design
  • Composite materials
  • Expected information gain
  • Importance sampling
  • Laplace approximation
  • Monte Carlo

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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