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Optimality criteria for probabilistic numerical methods

  • 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 the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative 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 average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.

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Author:Chris. J. Oates, Jon Cockayne, Dennis Prangle, T. J. Sullivan, Mark Girolami
Editor:F. J. Hickernell, P. Kritzer
Document Type:In Collection
Parent Title (English):Multivariate Algorithms and Information-Based Complexity
Publisher:De Gruyter
Year of first publication:2019
ArXiv Id:http://arxiv.org/abs/1901.04326