Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.
Mots-clés : epistemic uncertainty, aleatoric uncertainty, generalized polynomial chaos, relative entropy, uncertainty quantification, spectral methods, stochastic differential equations, Monte Carlo integration, stochastic collocation method, quadrature
@article{M2AN_2013__47_3_635_0,
author = {Chowdhary, Kamaljit and Dupuis, Paul},
title = {Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {635--662},
publisher = {EDP-Sciences},
volume = {47},
number = {3},
year = {2013},
doi = {10.1051/m2an/2012038},
mrnumber = {3056403},
zbl = {1266.65009},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2012038/}
}
TY - JOUR AU - Chowdhary, Kamaljit AU - Dupuis, Paul TI - Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 635 EP - 662 VL - 47 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2012038/ DO - 10.1051/m2an/2012038 LA - en ID - M2AN_2013__47_3_635_0 ER -
%0 Journal Article %A Chowdhary, Kamaljit %A Dupuis, Paul %T Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 635-662 %V 47 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2012038/ %R 10.1051/m2an/2012038 %G en %F M2AN_2013__47_3_635_0
Chowdhary, Kamaljit; Dupuis, Paul. Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 3, pp. 635-662. doi : 10.1051/m2an/2012038. http://archive.numdam.org/articles/10.1051/m2an/2012038/
[1] , and , Robustness and risk sensitive filtering. IEEE Trans. Auto. Control 3 (2002) 451-461. | MR
[2] and , A Weak Convergence Approach to the Theory of Large Deviations. John Wiley & Sons, New York (1997). | MR | Zbl
[3] , and , Robust properties of risk-sensitive control. Math. Control Signals Syst. 13 (2000) 318-332. | MR | Zbl
[4] and , Efficient algorithms for mixed aleatory-epistemic uncertainty quantification with applications to radiation-hardened electronics. Technical report, Sandia National Laboratories (2009).
[5] and , Spectral Methods for Uncertainty Quantification. Springer, New York (2010). | MR | Zbl
[6] , Large Deviations and Applications. CBMS-NSF Regional Conference Series in Mathematics. SIAM, Philadelphia (1984). | MR | Zbl
[7] , Efficient collocational approach for parametric uncertianty analysis. J. Comput. Phys. 2 (2007) 293-309. | MR | Zbl
[8] , Fast numerical methods for stochastic computations. Commun. Comput. Phys. 5 (2009) 242-272. | MR
[9] and , High-order collocation methods for differential equations with random inputs. Soc. Industrial Appl. Math. 27 (2005) 1118-1139. | MR | Zbl
[10] , and , Numerical approach for quantification of epistemic uncertainty. Commun. Comput. Phys. 229 (2010) 4648-4663. | MR | Zbl
[11] and , The Weiner-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24 (2002) 619-644. | MR | Zbl
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