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.

Classification: 41A10, 60H35, 65C30, 65C50

Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {47}, number = {3}, year = {2013}, pages = {635-662}, doi = {10.1051/m2an/2012038}, zbl = {1266.65009}, mrnumber = {3056403}, language = {en}, url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, pp. 635-662. doi : 10.1051/m2an/2012038. http://www.numdam.org/item/M2AN_2013__47_3_635_0/

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