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A modern retrospective on probabilistic numerics

Lookup NU author(s): Professor Chris OatesORCiD

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Abstract

This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern formal treatment. We highlight in particular the parallel contributions of Sul'din and Larkin in the 1960s and how their pioneering early ideas have reached a degree of maturity in the intervening period, mediated by paradigms such as average-case analysis and information-based complexity. We provide a subjective assessment of the state of research in probabilistic numerics and highlight some difficulties to be addressed by future works.

Publication metadata

Author(s): Oates CJ, Sullivan TJ

Publication type: Article

Publication status: Published

Journal: Statistics and Computing

Year: 2019

Volume: 29

Pages: 1335–1351

Print publication date: 01/11/2019

Online publication date: 04/10/2017

Acceptance date: 01/03/2019

Date deposited: 09/05/2019

ISSN (print): 0960-3174

ISSN (electronic): 1573-1375

Publisher: Springer US

URL: https://doi.org/10.1007/s11222-019-09902-z

DOI: 10.1007/s11222-019-09902-z

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