A modern retrospective on probabilistic numerics-Reference-Cited by-同舟云学术

A modern retrospective on probabilistic numerics

Published:2019-10-04 Issue:6 Volume:29 Page:1335-1351
ISSN:0960-3174
Container-title:Statistics and Computing
language:en
Short-container-title:Stat Comput

Author:

Oates C. J.,Sullivan T. J.

Abstract

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

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′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.

Funder

Newcastle University

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Statistics and Probability,Theoretical Computer Science

Link

http://link.springer.com/content/pdf/10.1007/s11222-019-09902-z.pdf

Reference156 articles.

1. Abdulle, A., Garegnani, G.: Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration (2018). arXiv:1801.01340

2. Acerbi, L.: Variational Bayesian Monte Carlo. In: 32nd Conference on Neural Information Processing Systems (NeurIPS 2018) (2018). https://papers.nips.cc/paper/8043-variational-bayesian-monte-carlo

3. Barlow, J.L., Bareiss, E.H.: Probabilistic error analysis of Gaussian elimination in floating point and logarithmic arithmetic. Computing 34(4), 349–364 (1985). https://doi.org/10.1007/BF02251834

4. Bartels, S., Hennig, P.: Probabilistic approximate least-squares. In: Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, volume 51 of Proceedings of Machine Learning Research, pp. 676–684 (2016). http://proceedings.mlr.press/v51/bartels16.pdf

5. Bartels, S., Cockayne, J., Ipsen, I.C.F., Hennig, P.: Probabilistic linear solvers: a unifying view. Stat. Comput. (2019). https://doi.org/10.1007/s11222-019-09897-7

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