Optimal Uncertainty Quantification
Authors:
- H. OwhadiHOH. Owhadi
- C. ScovelCSC. Scovel
- T. J. SullivanTST. J. Sullivan
- M. McKernsMMM. McKerns
- M. OrtizMOM. Ortiz
- 1 January 2013
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Review
- Vol. 55 (2) , 271-345
Abstract
We propose a rigorous framework for uncertainty quantification (UQ) in which the UQ objectives and its assumptions/information set are brought to the forefront. This framework, which we call optimal uncertainty quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions they have finite-dimensional reductions. As an application, we develop optimal concentration inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, these results show that ...Keywords
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This publication has 65 references indexed in Scilit:
- Rigorous model-based uncertainty quantification with application to terminal ballistics—Part II. Systems with uncontrollable inputs and large scatterJournal of the Mechanics and Physics of Solids, 2012
- Bayesian system identification based on probability logicStructural Control and Health Monitoring, 2010
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input DataSIAM Review, 2010
- Sparse high order FEM for elliptic sPDEsComputer Methods in Applied Mechanics and Engineering, 2009
- Optimal Hoeffding-like inequalities under a symmetry assumptionStatistics, 2006
- Optimal Inequalities in Probability Theory: A Convex Optimization ApproachSIAM Journal on Optimization, 2005
- On Hoeffding’s inequalitiesThe Annals of Probability, 2004
- A sharp concentration inequality with applicationsRandom Structures & Algorithms, 2000
- Updating Models and Their Uncertainties. I: Bayesian Statistical FrameworkJournal of Engineering Mechanics, 1998
- The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalitiesProceedings of the American Mathematical Society, 1955