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Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol' indices estimation via a metamodeling…

Statistics Theory · Mathematics 2021-01-07 Ivan I. Panin

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these…

Computation · Statistics 2016-05-31 K. Konakli , B. Sudret

A new method for estimating Sobol' indices is proposed. The new method makes use of 3 independent input vectors rather than the usual 2. It attains much greater accuracy on problems where the target Sobol' index is small, even outperforming…

Methodology · Statistics 2012-04-24 Art B. Owen

Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to…

Analysis of PDEs · Mathematics 2012-01-16 Alexandre Janon , Maëlle Nodet , Clémentine Prieur

We describe a novel attribution method which is grounded in Sensitivity Analysis and uses Sobol indices. Beyond modeling the individual contributions of image regions, Sobol indices provide an efficient way to capture higher-order…

Computer Vision and Pattern Recognition · Computer Science 2022-02-17 Thomas Fel , Remi Cadene , Mathieu Chalvidal , Matthieu Cord , David Vigouroux , Thomas Serre

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…

Statistics Theory · Mathematics 2013-03-27 Alexandre Janon , Thierry Klein , Agnes Lagnoux-Renaudie , Maëlle Nodet , Clémentine Prieur

The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and…

Data Analysis, Statistics and Probability · Physics 2018-08-17 Joseph Hart , Pierre Gremaud

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This…

Applications · Statistics 2008-06-09 Bertrand Iooss , Mathieu Ribatet

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…

Methodology · Statistics 2008-02-08 Amandine Marrel , Bertrand Iooss , Beatrice Laurent , Olivier Roustant

The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu…

Computation · Statistics 2011-04-22 Amandine Marrel , Bertrand Iooss , Michel Jullien , Beatrice Laurent , Elena Volkova

The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally…

Numerical Analysis · Mathematics 2016-06-03 Sergei Kucherenko , Shufang Song

Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…

Numerical Analysis · Mathematics 2017-01-20 Ivan Dimov , Rayna Georgieva

Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying…

Computation · Statistics 2016-11-29 Joseph L. Hart , Alen Alexanderian , Pierre A. Gremaud

Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the…

Statistics Theory · Mathematics 2024-03-20 Henri Mermoz Kouye , Gildas Mazo

It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we…

Machine Learning · Statistics 2026-03-23 Gildas Mazo

Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…

Numerical Analysis · Mathematics 2020-12-23 Chun Yui Wong , Pranay Seshadri , Geoffrey T. Parks

Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the…

Statistics Theory · Mathematics 2025-03-25 Robert A. Milton , Solomon F. Brown

Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the…

Statistics Theory · Mathematics 2020-01-22 Viet Chi Tran , Gwenaëlle Castellan , Anthony Cousien , Chi Tran

We propose a new importance sampling framework for the estimation and analysis of Sobol' indices. We focus on the estimation of the conditional second-moment quantity underlying these indices, which is the most challenging term to estimate.…

Statistics Theory · Mathematics 2026-03-03 Haythem Boucharif , Jérôme Morio , Paul Rochet
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