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 Probability Surveys > Vol. 10 (2013) open journal systems 

On spectral methods for variance based sensitivity analysis

Alen Alexanderian, The University of Texas at Austin

Consider a mathematical model with a finite number of random parameters. Variance based sensitivity analysis provides a framework to characterize the contribution of the individual parameters to the total variance of the model response. We consider the spectral methods for variance based sensitivity analysis which utilize representations of square integrable random variables in a generalized polynomial chaos basis. Taking a measure theoretic point of view, we provide a rigorous and at the same time intuitive perspective on the spectral methods for variance based sensitivity analysis. Moreover, we discuss approximation errors incurred by fixing inessential random parameters, when approximating functions with generalized polynomial chaos expansions.

Keywords: Variance based sensitivity analysis, analysis of variance, spectral methods, generalized polynomial chaos, orthogonal polynomials, conditional expectation.

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Alexanderian, Alen, On spectral methods for variance based sensitivity analysis, Probability Surveys, 10, (2013), 51-68 (electronic). DOI: 10.1214/13-PS219.


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