TY - JOUR
T1 - Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty
AU - Bartuska, Arved
AU - Espath, Luis
AU - Tempone, Raul
N1 - 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).
PY - 2022/7/15
Y1 - 2022/7/15
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/678014
UR - https://linkinghub.elsevier.com/retrieve/pii/S0045782522004194
UR - http://www.scopus.com/inward/record.url?scp=85134238034&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2022.115320
DO - 10.1016/j.cma.2022.115320
M3 - Article
SN - 0045-7825
VL - 399
SP - 115320
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -