Probabilistic Integration: A Role in Statistical Computation?

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Title: Probabilistic Integration: A Role in Statistical Computation?
Authors: Briol, F-X
Oates, CJ
Girolami, M
Osborne, MA
Sejdinovic, D
Item Type: Journal Article
Abstract: A research frontier has emerged in scientific computation, wherein numerical 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. 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 presence of an unknown numerical error. Our main technical contribution is to establish, for the first time, rates of posterior contraction for these methods. These show that probabilistic integrators can in principle enjoy the "best of both worlds", leveraging the sampling efficiency of Monte Carlo methods whilst providing a principled route to assess the impact of numerical error on scientific conclusions. 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.
Issue Date: 1-Feb-2019
Date of Acceptance: 25-May-2018
URI: http://hdl.handle.net/10044/1/67126
ISSN: 0883-4237
Publisher: Institute of Mathematical Statistics
Journal / Book Title: Statistical Science
Copyright Statement: This paper is embargoed until publication.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/K034154/1
Keywords: stat.ML
cs.NA
math.NA
math.ST
stat.CO
stat.TH
0104 Statistics
Statistics & Probability
Notes: Several improvements suggested by reviewers, including additional experiments on uncertainty quantification properties. Change of title: previously "Probabilistic Integration: A Role for Statisticians in Numerical Analysis?"
Embargo Date: publication subject to indefinite embargo
Open Access location: https://arxiv.org/pdf/1512.00933.pdf
Appears in Collections:Mathematics
Statistics



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