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Optimality criteria for probabilistic numerical methods
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Oates, C.J., Cockayne, J., Prangle, D., Sullivan, T. J. and Girolami, M. (2020) Optimality criteria for probabilistic numerical methods. In: Hickernell, Fred J. and Kritzer, Peter , (eds.) Multivariate Algorithms and Information-Based Complexity. Radon Series on Computational and Applied Mathematics (27). De Gruyter, pp. 65-88. ISBN 9783110633115
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Official URL: http://dx.doi.org/10.1515/9783110635461-005
Abstract
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches from the decision-theoretic framework are neither appropriate nor sufficient. Instead, we consider a particular optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an averagecase- optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes, in which optimal probabilistic numerical methods can be developed.
Item Type: | Book Item | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Series Name: | Radon Series on Computational and Applied Mathematics | ||||||
Publisher: | De Gruyter | ||||||
ISBN: | 9783110633115 | ||||||
Book Title: | Multivariate Algorithms and Information-Based Complexity | ||||||
Editor: | Hickernell, Fred J. and Kritzer, Peter | ||||||
Official Date: | 18 May 2020 | ||||||
Dates: |
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Number: | 27 | ||||||
Page Range: | pp. 65-88 | ||||||
DOI: | 10.1515/9783110635461-005 | ||||||
Status: | Not Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 14 July 2020 |
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