Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

By I. M. Soboĺ. 2001

5,285 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

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Citations in the corpus

Sensitivity-guided reduction of parametric dimensionality for multi-objective calibration of watershed models (2009, background): “Formore detail on Sobol’smethod, see Sobol’ [28,29], Hall et al.”
Learning Global Additive Explanations for Neural Nets Using Model Distillation (2018, methodology): “1 ADDITIVE F̂ Global additive explanations have been used to analyze inputs to complex, nonlinear mathematical models and computer simulations (Sobol, 2001), analyze how hyperparameters affect the performance of machine learning algorithms (Hutter et al.”
A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures (2014, neutral): “obal sensitivity analysis constitutes the study of howthe output variance from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [25]. There exist a multitudes of methods or techniques for calculating the global sensitivity indic”
Asymptotic normality and efficiency of two Sobol index estimators (2013, methodology): “ve been developed by the experimental sciences and engineeringcommunities. This includes the FAST methods (see for example[4], [31] and references therein) and the Sobol pick-freeze (SPF) scheme (see [27, 28]). In SPF a Sobol index is viewed as the regression coeﬃcient between the output of the mode”
Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion (2011, methodology): “PCE or SPCE methodology are the so-called Sobol indices [27] for estimating the sensitivity indices.”
Variance decomposition and global sensitivity for structural systems (2010, background): “More details about the assumptions and theory can be found in the original publications [1,2,8,9].”
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis (2011, methodology): “The Monte Carlo algorithm was proposed by Sobol [4], and has been later improved by the Quasi Monte Carlo technique, performed by Owen [5].”
Sensitivity Analysis in Probabilistic Structural Design: A Comparison of Selected Techniques (2020, methodology): “Sobol’s sensitivity indices [12,13] (in short, Sobol’s indices).”
Explainable AI: A Review of Machine Learning Interpretability Methods (2020, methodology): “An output variance sensitivity analysis that is based on the ANOVA decomposition was formalised by Sobol, who proposed the approximation of sensitivity indices of first and higher order while using Monte-Carlo methods [101], while Saltelli [102] and”
Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site (2008, methodology): “This variance-based method uses the so-called ANOVA-representation of square integrable functions developed by Sobol (for example, Sobol 2001 ).”