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Probabilistic integration: A role in statistical computation?

Briol, FX; Oates, CJ; Girolami, M; Osborne, MA; Sejdinovic, D; (2019) Probabilistic integration: A role in statistical computation? Statistical Science , 34 (1) pp. 1-22. 10.1214/18-STS660. Green open access

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Abstract

A research frontier has emerged in scientific computation, wherein discretisation error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly deterministic) computational work-flow, in order to assess the impact of discretisation error on the computer output. This paper examines the case for probabilistic numerical methods in routine statistical computation. Our focus is on numerical integration, where a probabilistic integrator is equipped with a full distribution over its output that reflects the fact that the integrand has been discretised. Our main technical contribution is to establish, for the first time, rates of posterior contraction for one such method. Several substantial applications are provided for illustration and critical evaluation, including examples from statistical modelling, computer graphics and a computer model for an oil reservoir.

Type: Article
Title: Probabilistic integration: A role in statistical computation?
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/18-STS660
Publisher version: http://dx.doi.org/10.1214/18-STS660
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: Computational statistics, nonparametric statistics, probabilistic numerics, uncertainty quantification
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
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
URI: https://discovery.ucl.ac.uk/id/eprint/10079226
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