A Bayes–Sard Cubature Method

Toni Karvonen, Chris J. Oates, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes–Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are well-established. This is achieved by considering a Gaussian process model for the integrand whose mean is a parametric regression model, with an improper prior on each regression coefficient. The features in the regression model consist of test functions which are guaranteed to be exactly integrated, with remaining degrees of freedom afforded to the non-parametric part. The asymptotic convergence of the Bayes–Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 31
Subtitle of host publicationProceedings of NIPS2017
PublisherCurran Associates, Inc.
Number of pages12
Publication statusPublished - Dec 2018
MoE publication typeA4 Article in a conference publication
EventConference on Neural Information Processing Systems - Palais des Congrès de Montréal, Montréal, Canada
Duration: 2 Dec 20188 Dec 2018
Conference number: 32

Publication series

NameAdvances in neural information processing systems
PublisherCurran Associates
ISSN (Print)1049-5258


ConferenceConference on Neural Information Processing Systems
Abbreviated titleNeurIPS
Internet address

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