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Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification∗

Published online by Cambridge University Press:  29 March 2013

Kamaljit Chowdhary  and
Paul Dupuis
Kamaljit Chowdhary
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA. [email protected]
Paul Dupuis
Affiliation:
Lefschetz Center for Dynamical Systems, Division of Applied Mathematics,Brown University, Providence, RI, 02912, USA; [email protected]
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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.

Keywords

Epistemic uncertaintyaleatoric uncertaintygeneralized polynomial chaosrelative entropyuncertainty quantificationspectral methodsstochastic differential equationsmonte Carlo integrationstochastic collocation methodquadrature
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 3 , May 2013 , pp. 635 - 662
Copyright
© EDP Sciences, SMAI, 2013

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