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February 2019 Probabilistic Integration: A Role in Statistical Computation?
François-Xavier Briol, Chris J. Oates, Mark Girolami, Michael A. Osborne, Dino Sejdinovic
Statist. Sci. 34(1): 1-22 (February 2019). DOI: 10.1214/18-STS660


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.


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François-Xavier Briol. Chris J. Oates. Mark Girolami. Michael A. Osborne. Dino Sejdinovic. "Probabilistic Integration: A Role in Statistical Computation?." Statist. Sci. 34 (1) 1 - 22, February 2019.


Published: February 2019
First available in Project Euclid: 12 April 2019

zbMATH: 07110669
MathSciNet: MR3938958
Digital Object Identifier: 10.1214/18-STS660

Keywords: computational statistics , nonparametric statistics , probabilistic numerics , uncertainty quantification

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2019
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