Theorems and examples on high dimensional model representation

By Ilya M. Sobol. Reliability Engineering & System Safety, 2003

471 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/36ff649cac77927cddb3f541bf653f5f88737536

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions (2009, background): “…also known as analysis of variance ANOVA Efron and Stein 1981 or high-dimensional model representation HDMR Li et al. 2002; Rabitz and Alis 1999; Sobol 2003 , represents a finite, hierarchical, and convergent expansion of a multivariate output function Rahman 2008 y x = y0 + i=1 N yi xi +…”
An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks (2015, methodology): “In addition, global sensitivity indices (also called Sobol indices) are computed from the ratio of each component function’s variance to that of V (x) [46], i.”
Polynomial chaos expansion in structural dynamics: Accelerating the convergence of the first two statistical moment sequences (2015, background): “Polynomial Chaos (PC) expansion [10–12], High Dimensional Model Reduction (HDMR) [13–15] and Gaussian Process (GP) Emulators [16–18] have been developed for any level of uncertainty.”
A Review on Global Sensitivity Analysis Methods (2014, unknown): “(8)) gives us what is missing in the SA (Sobol [84]).”
Global sensitivity analysis using polynomial chaos expansions (2008, background): “Let us consider the so-called Sobol’ function (Sobol’, 2003): where the input variables X i , i = 1 , . . . , q are uniformly distributed over [0 , 1] and a i ’s are non negative.”
An efficient lightweight design strategy for body-in-white based on implicit parameterization technique (2017, methodology): “Among many different GSA methods, the Sobol’s method (Sobol’ 2001, 2003) is able to provide a robust method for the derivation of the input parameters in non-linear models, taking the effect of parameter combinations and higher order effects on the response into account (Bojanowski and Kulak 2011;…”