Optimality Criteria for Probabilistic Numerical Methods
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 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.
Cite
@article{arxiv.1901.04326,
title = {Optimality Criteria for Probabilistic Numerical Methods},
author = {Chris. J. Oates and Jon Cockayne and Dennis Prangle and T. J. Sullivan and Mark Girolami},
journal= {arXiv preprint arXiv:1901.04326},
year = {2020}
}
Comments
Prepared for the proceedings of the RICAM workshop on Multivariate Algorithms and Information-Based Complexity, November 2018