Statistical Science

Probabilistic Integration: A Role in Statistical Computation?

François-Xavier Briol, Chris J. Oates, Mark Girolami, Michael A. Osborne, and Dino Sejdinovic

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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.

Article information

Statist. Sci., Volume 34, Number 1 (2019), 1-22.

First available in Project Euclid: 12 April 2019

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Computational statistics nonparametric statistics probabilistic numerics uncertainty quantification


Briol, François-Xavier; Oates, Chris J.; Girolami, Mark; Osborne, Michael A.; Sejdinovic, Dino. Probabilistic Integration: A Role in Statistical Computation?. Statist. Sci. 34 (2019), no. 1, 1--22. doi:10.1214/18-STS660.

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See also

  • Comment on "Probabilistic Integration: A Role in Statistical Computation?".
  • Comment: Unreasonable Effectiveness of Monte Carlo.
  • Comment on "Probabilistic Integration: A Role in Statistical Computation?".
  • Rejoinder: Probabilistic Integration: A Role in Statistical Computation?.

Supplemental materials

  • Supplement to “Probabilistic Integration: A Role in Statistical Computation?”. This supplement contains all proofs as well as additional details relating to the numerical experiments.