Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty

Arved Bartuska, Luis Espath, Raul Tempone

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, which are parameters that contribute to the overall uncertainty of the system but are of no interest in the Bayesian design framework, this introduces a second inner loop. We propose and derive a small-noise approximation for this additional inner loop. The computational cost of our method can be further reduced by applying a Laplace approximation to the remaining inner loop. Thus, we present two methods, the small-noise double-loop Monte Carlo and small-noise Monte Carlo Laplace methods. Moreover, we demonstrate that the total complexity of these two approaches remains comparable to the case without nuisance uncertainty. To assess the efficiency of these methods, we present three examples, and the last example includes the partial differential equation for the electrical impedance tomography experiment for composite laminate materials.
Original languageEnglish (US)
Pages (from-to)115320
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Jul 15 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-09-14
Acknowledged KAUST grant number(s): OSR-2019-CRG8-4033
Acknowledgements: This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia Office of Sponsored Research (OSR) under Award No. OSR-2019-CRG8-4033, the Alexander von Humboldt Foundation, Germany, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Germany - 333849990/GRK2379 (IRTG Modern Inverse Problems).

ASJC Scopus subject areas

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


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