Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design

Joakim Beck, Ben Mansour Dia, Luis Espath, Raul Tempone

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14 Scopus citations


An optimal experimental set-up maximizes the value of data for statistical inferences. The efficiency of strategies for finding optimal experimental set-ups is particularly important for experiments that are time-consuming or expensive to perform. In the situation when the experiments are modeled by partial differential equations (PDEs), multilevel methods have been proven to reduce the computational complexity of their single-level counterparts when estimating expected values. For a setting where PDEs can model experiments, we propose two multilevel methods for estimating a popular criterion known as the expected information gain (EIG) in Bayesian optimal experimental design. We propose a multilevel double loop Monte Carlo, which is a multilevel strategy with double loop Monte Carlo, and a multilevel double loop stochastic collocation, which performs a high-dimensional integration on sparse grids. For both methods, the Laplace approximation is used for importance sampling that significantly reduces the computational work of estimating inner expectations. The values of the method parameters are determined by minimizing the computational work, subject to satisfying the desired error tolerance. The efficiencies of the methods are demonstrated by estimating EIG for inference of the fiber orientation in composite laminate materials from an electrical impedance tomography experiment.
Original languageEnglish (US)
JournalInternational Journal for Numerical Methods in Engineering
StatePublished - Apr 17 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): URF/1/2281-01-01, URF/1/2584-01-01
Acknowledgements: The research reported in this publication was supported by funding from King Abdullah University of Science and Tech-nology (KAUST) Office of Sponsored Research (OSR) under award numbers URF/1/2281-01-01 and URF/1/2584-01-01 in the KAUST Competitive Research Grants Program-Round 3 and 4, respectively, and the Alexander von Humboldt Foun-dation. J. Beck, L.F.R. Espath, and R. Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.


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