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

Bartuska, Arved; Espath, Luis; Tempone, Raúl

Abstract

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.

Citation

Bartuska, A., Espath, L., & Tempone, R. (2022). Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty. Computer Methods in Applied Mechanics and Engineering, 399, Article 115320. https://doi.org/10.1016/j.cma.2022.115320

• Journal Article Type: Article
• Acceptance Date: Jun 28, 2022
• Online Publication Date: Jul 15, 2022
• Publication Date: Sep 1, 2022
• Deposit Date: Jul 25, 2022
• Publicly Available Date: Jul 16, 2023
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Electronic ISSN: 1879-2138
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 399
• Article Number: 115320
• DOI: https://doi.org/10.1016/j.cma.2022.115320
• Keywords: Computer Science Applications; General Physics and Astronomy; Mechanical Engineering; Mechanics of Materials; Computational Mechanics
• Public URL: https://nottingham-repository.worktribe.com/output/9400253
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0045782522004194?via%3Dihub