Probabilistic integration: A role in statistical computation?

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dc.contributor.authorBriol, F.X.
dc.contributor.authorOates, C.J.
dc.contributor.authorGirolami, M.
dc.contributor.authorOsborne, M.A.
dc.contributor.authorSejdinovic, D.
dc.date.issued2019
dc.description.abstractA 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.
dc.description.statementofresponsibilityFrançois-Xavier Briol, Chris J. Oates, Mark Girolami, Michael A. Osborne and Dino Sejdinovic
dc.identifier.citationStatistical Science: a review journal, 2019; 34(1):1-22
dc.identifier.doi10.1214/18-STS660
dc.identifier.issn0883-4237
dc.identifier.issn2168-8745
dc.identifier.orcidSejdinovic, D. [0000-0001-5547-9213]
dc.identifier.urihttps://hdl.handle.net/2440/136933
dc.language.isoen
dc.publisherInstitute of Mathematical Statistics
dc.relation.granthttp://purl.org/au-research/grants/arc/CE140100049
dc.rights© Institute of Mathematical Statistics, 2019. Open Access
dc.source.urihttps://doi.org/10.1214/18-sts660
dc.subjectComputational statistics; nonparametric statistics; probabilistic numerics; uncertainty quantification
dc.titleProbabilistic integration: A role in statistical computation?
dc.typeJournal article
pubs.publication-statusPublished

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