Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations

Quan Long, Marco Scavino, Raul Tempone, Suojin Wang

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

Shannon-type expected information gain can be used to evaluate the relevance of a proposed experiment subjected to uncertainty. The estimation of such gain, however, relies on a double-loop integration. Moreover, its numerical integration in multi-dimensional cases, e.g., when using Monte Carlo sampling methods, is therefore computationally too expensive for realistic physical models, especially for those involving the solution of partial differential equations. In this work, we present a new methodology, based on the Laplace approximation for the integration of the posterior probability density function (pdf), to accelerate the estimation of the expected information gains in the model parameters and predictive quantities of interest. We obtain a closed-form approximation of the inner integral and the corresponding dominant error term in the cases where parameters are determined by the experiment, such that only a single-loop integration is needed to carry out the estimation of the expected information gain. To deal with the issue of dimensionality in a complex problem, we use a sparse quadrature for the integration over the prior pdf. We demonstrate the accuracy, efficiency and robustness of the proposed method via several nonlinear numerical examples, including the designs of the scalar parameter in a one-dimensional cubic polynomial function, the design of the same scalar in a modified function with two indistinguishable parameters, the resolution width and measurement time for a blurred single peak spectrum, and the boundary source locations for impedance tomography in a square domain. © 2013 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)24-39
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Volume259
DOIs
StatePublished - Jun 2013

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications

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