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Uncertainty quantification via codimension-one partitioning
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Sullivan, T., Topcu, U., McKerns, M. and Owhadi, H. (2010) Uncertainty quantification via codimension-one partitioning. International Journal for Numerical Methods in Engineering, Vol.85 (No.12). pp. 1499-1521. doi:10.1002/nme.3030 ISSN 0029-5981.
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Official URL: http://dx.doi.org/10.1002/nme.3030
Abstract
We consider uncertainty quantification in the context of certification, i.e. showing that the probability of some ‘failure’ event is acceptably small. In this paper, we derive a new method for rigorous uncertainty quantification and conservative certification by combining McDiarmid's inequality with input domain partitioning and a new concentration-of-measure inequality. We show that arbitrarily sharp upper bounds on the probability of failure can be obtained by partitioning the input parameter space appropriately; in contrast, the bound provided by McDiarmid's inequality is usually not sharp. We prove an error estimate for the method (Proposition 3.2); we define a codimension-one recursive partitioning scheme and prove its convergence properties (Theorem 4.1); finally, we apply a new concentration-of-measure inequality to give confidence levels when empirical means are used in place of exact ones (Section 5).
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | International Journal for Numerical Methods in Engineering | ||||
Publisher: | John Wiley & Sons Ltd. | ||||
ISSN: | 0029-5981 | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.85 | ||||
Number: | No.12 | ||||
Page Range: | pp. 1499-1521 | ||||
DOI: | 10.1002/nme.3030 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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