Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

Kamaljit Chowdhary; Paul Dupuis

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 3, page 635-662
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Chowdhary, Kamaljit, and Dupuis, Paul. "Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.3 (2013): 635-662. <http://eudml.org/doc/273298>.

@article{Chowdhary2013,
abstract = {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.},
author = {Chowdhary, Kamaljit, Dupuis, Paul},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {epistemic uncertainty; aleatoric uncertainty; generalized polynomial chaos; relative entropy; uncertainty quantification; spectral methods; stochastic differential equations; Monte Carlo integration; stochastic collocation method; quadrature},
language = {eng},
number = {3},
pages = {635-662},
publisher = {EDP-Sciences},
title = {Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification},
url = {http://eudml.org/doc/273298},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 3
SP - 635
EP - 662
AB - 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.
LA - eng
KW - epistemic uncertainty; aleatoric uncertainty; generalized polynomial chaos; relative entropy; uncertainty quantification; spectral methods; stochastic differential equations; Monte Carlo integration; stochastic collocation method; quadrature
UR - http://eudml.org/doc/273298
ER -

References

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  8. [8] D. Xiu, Fast numerical methods for stochastic computations. Commun. Comput. Phys.5 (2009) 242–272. MR2513686
  9. [9] D. Xiu and J. Hesthaven, High-order collocation methods for differential equations with random inputs. Soc. Industrial Appl. Math.27 (2005) 1118–1139. Zbl1091.65006MR2199923
  10. [10] D. Xiu, J. Jakeman and M. Eldred, Numerical approach for quantification of epistemic uncertainty. Commun. Comput. Phys.229 (2010) 4648–4663. Zbl1204.65008MR2643667
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