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Uncertainty Quantification for Approximate p-Quantiles for Physical Models with Stochastic Inputs

Daniel Elfverson ; Donald J. Estep ; Fredrik Hellman ; Axel Målqvist (Institutionen för matematiska vetenskaper, matematik)
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION (2166-2525). Vol. 2 (2014), 1, p. 826-850.
[Artikel, refereegranskad vetenskaplig]

We consider the problem of estimating the p-quantile for a given functional evaluated on solutions of a deterministic model in which model input is subject to stochastic variation. We derive upper and lower bounding estimators of the p-quantile. We perform an a posteriori error analysis for the p-quantile estimators that takes into account the effects of both the stochastic sampling error and the deterministic numerical solution error and yields a computational error bound for the estimators. We also analyze the asymptotic convergence properties of the p-quantile estimator bounds in the limit of large sample size and decreasing numerical error and describe algorithms for computing an estimator of the p-quantile with a desired accuracy in a computationally efficient fashion. One algorithm exploits the fact that the accuracy of only a subset of sample values significantly affects the accuracy of a p-quantile estimator resulting in a significant gain in computational efficiency. We conclude with a number of numerical examples, including an application to Darcy flow in porous media.



Denna post skapades 2017-12-04.
CPL Pubid: 253544

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur