Journal ArticleDOI
Theorems and examples on high dimensional model representation
TLDR
Mathematical models described by multivariable functions f(x) where x=(x1,…,xn) are investigated, and an attempt can be made to construct a low order approximation to the model using values of f( x) only.About:
This article is published in Reliability Engineering & System Safety.The article was published on 2003-02-01. It has received 415 citations till now. The article focuses on the topics: High-dimensional model representation & Function of several real variables.read more
Citations
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Journal ArticleDOI
Global sensitivity analysis using polynomial chaos expansions
TL;DR: In this article, generalized polynomial chaos expansions (PCE) are used to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients.
Reliability Engineering and System Safety
TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.
Journal ArticleDOI
A new uncertainty importance measure
TL;DR: A global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters.
Book ChapterDOI
A Review on Global Sensitivity Analysis Methods
Bertrand Iooss,Paul Lemaître +1 more
TL;DR: In this article, a review of various global sensitivity analysis methods of model output is presented, in a complete methodological framework, in which three kinds of methods are distinguished: the screening (coarse sorting of the most influential inputs among a large number), the measures of importance (quantitative sensitivity indices) and the deep exploration of the model behaviour (measuring the effects of inputs on their all variation range).
Journal ArticleDOI
Sensitivity analysis: A review of recent advances
TL;DR: This work investigates in detail the methodological issues concerning the crucial step of correctly interpreting the results of a sensitivity analysis, and presents recent results that permit the estimation of global sensitivity measures by post-processing the sample generated by a traditional Monte Carlo simulation.
References
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Journal ArticleDOI
Sensitivity Measures, ANOVA-like Techniques and the Use of Bootstrap
TL;DR: In this paper, the authors compared Sobol' sensitivity indices, used in variance based global sensitivity analysis of model output, with the Analysis of Variance in classical factorial design, and presented a bootstrap approach to produce a confidence interval for the true,unknown indices.
Journal ArticleDOI
Efficient input-output model representations
TL;DR: Two types of HDMR's are presented in this paper: ANOVA-HDMR is the same as the analysis of variance (ANOVA) decomposition used in statistics, and another cut- HDMR will be shown to be computationally more efficient than the ANOVA decomposition.
Sensitivity Analysis for Nonlinear Mathematical Models. Numerical ExperienceSensitivity Analysis for Nonlinear Mathematical Models. Numerical Experience
Saltelli Andrea,Sobol I.m. +1 more
Journal ArticleDOI
About the use of rank transformation in sensitivity analysis of model output
Andrea Saltelli,I. M. Sobol +1 more
TL;DR: In this article, the effect of rank transformations on the outcome of a sensitivity analysis is explored, by way of practical examples, and an attempt is made to identify trends, and to correlate these effects to a model taxonomy.