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Multilevel Bayesian Quadrature

Li, Kaiyu; Giles, Daniel; Karvonen, Toni; Guillas, Serge; Briol, François-Xavier; (2022) Multilevel Bayesian Quadrature. arXiv: Ithaca, NY, USA. Green open access

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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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