Sensitivity Estimates for Nonlinear Mathematical Models

By Ilya M. Sobol. 1993

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Citations in the corpus

Tabular Benchmarks for Joint Architecture and Hyperparameter Optimization (2019, methodology): “We now analyze how the different hyperparameters affect the ﬁnal performance, ﬁrst globally with help of the functional ANOVA (Sobol, 1993; Hutter et al., 2014)”
Theorems and examples on high dimensional model representation (2003, methodology): “[8] is the computation algorithm that allows a direct estimation of global sensitivity indices using values of f(x ) only.”
An efficient lightweight design strategy for body-in-white based on implicit parameterization technique (2017, unknown): “(Sobol’ 1993), Di can be calculated as Di ¼ Z f xð Þ f xi; x0−ið Þdxdx0−i− f 20 where dx0−i ¼ ∏ k≠i dx 0 k ; k ¼ 1;⋯; n ðA:8Þ Similarly, D-i can be calculated as D−i ¼ Z f xð Þ f x0i; x‐i dxdx 0 i− f 2 0 ðA:9Þ For computational expensive engineering problems, multi-dimensional integrals are…”
Implementation and Application of a Root Growth Module in HYDRUS (2018, methodology): “Sobol¢ (1993) proposed that the total variance of the model output can be decomposed into component variances of individual parameters and their interactions.”
Global uncertainty assessments by high dimensional model representations (HDMR) (2002, background): “For instance, distinct sets of Monte Carlo random samples of f(xi; xi) at di1erent <xed values of xi are needed to determine fi(xi) (Sobol, 1993).”
Quasi-regression for visualization and interpretation of black box functions (2002, background): “The importance of the subsetu of input variables can be described by either 2u =Xv u 2v ; or, 2u = Xv\u6=; 2v : Normalized versions, 2u= 2 and 2u= 2, are the global sensitivity indices of Sobol’ (1993).”
Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis (2011, unknown): “Following this approach, Sobol [3] introduces variability measures, the so called Sobol sensitivity indices, to estimate the contribution of each input on a system.”
On the Relative Importance of Input Factors in Mathematical Models (2002, methodology): “adds up to the total unconditional variance V (Sobol’ 1990).”
Model Performance Sensitivity to Objective Function during Automated Calibrations (2012, methodology): “Automated model calibration was performed to identify optimal values of 12 most sensitive streamflow parameters of SWAT that were previously identified by the author (Muleta 2012) using a global sensitivity analysis model known as Sobol (Sobol’ 1993).”