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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…

The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…

Statistics Theory · Mathematics 2019-11-26 Bertrand Iooss , Clémentine Prieur

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

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

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

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

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

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

We define and study a generalization of Sobol sensitivity indices for the case of a vector output.

Applications · Statistics 2013-04-18 Fabrice Gamboa , Alexandre Janon , Thierry Klein , Agnès Lagnoux

Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…

Computation · Statistics 2018-12-19 Joseph Hart , Pierre Gremaud

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

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

Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences via a global sensitivity analysis (GSA). However, these…

Methodology · Statistics 2014-12-04 Matthias De Lozzo , Amandine Marrel

In the context of air quality control, our objective is to quantify the impact of uncertain inputs such as meteorological conditions and traffic parameters on pollutant dispersion maps. It is worth noting that the majority of sensitivity…

This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this…

Applications · Statistics 2015-09-15 Mathilde Grandjacques , Alexandre Janon , Benoit Delinchant , Olivier Adrot

In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the…

Methodology · Statistics 2024-08-12 Thomas Most

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

In this paper, we study sensitivity indices for independent groups of variables and we look at the particular case of block-additive models. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can…

Statistics Theory · Mathematics 2018-12-12 Baptiste Broto , François Bachoc , Marine Depecker , Jean-Marc Martinez

Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specify (or implicitly assume), a probability distribution to model the uncertainty,…

Statistics Theory · Mathematics 2018-11-22 Joseph Hart , Pierre Gremaud

A variety of indices aim to quantify the impact of input variables on a response, typically the output from a complex computer code or black-box model. Most commonly used, the Sobol' index typically measures the influence of some inputs…

Statistics Theory · Mathematics 2025-07-22 Thierry Klein , Agnès Lagnoux , Paul Rochet , Thi Mong Ngoc Nguyen
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