Li, Kaiyu;
Giles, Daniel;
Karvonen, Toni;
Guillas, Serge;
Briol, François-Xavier;
(2022)
Multilevel Bayesian Quadrature.
arXiv: Ithaca, NY, USA.
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Abstract
Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We propose to further enhance multilevel Monte Carlo through Bayesian surrogate models of the integrand, focusing on Gaussian process models and the associated Bayesian quadrature estimators. We show using both theory and numerical experiments that our approach can lead to significant improvements in accuracy when the integrand is expensive and smooth, and when the dimensionality is small or moderate. We conclude the paper with a case study illustrating the potential impact of our method in landslide-generated tsunami modelling, where the cost of each integrand evaluation is typically too large for operational settings.
| Type: | Working / discussion paper |
|---|---|
| Title: | Multilevel Bayesian Quadrature |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.48550/arXiv.2210.08329 |
| Publisher version: | http://arxiv.org/abs/2210.08329v1 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | stat.ME, stat.ME |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10158239 |
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