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Published March 25, 2011 | public
Journal Article

Uncertainty quantification via codimension-one partitioning


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).

Additional Information

© 2010 John Wiley & Sons, Ltd. Received 3 March 2010; Revised 14 July 2010; Accepted 25 July 2010. Article first published online: 2 Sep. 2010. The authors wish to thank the other members of the California Institute of Technology's Predictive Science Academic Alliance Program (PSAAP) Uncertainty Quantification Group—Ali Lashgari, Bo Li and Michael Ortiz—for many stimulating discussions. They also thank the Caltech PSAAP Experimental Science Group—in particular, Marc Adams, Leslie Lamberson and Jonathan Mihaly—for formula (23). We thank the anonymous referees for their helpful comments. Calculations for this paper were performed using the Mystic optimization framework [32]. The authors also acknowledge portions of this work developed as part of the PSAAP project, supported by the United States Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613, and U. Topcu acknowledges partial support from the Boeing Corporation.

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