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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…
In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the popularity of Sobol's approach relies on the simplicity of…
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…
Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sensitivity indices, so-called Shapley effects have recently…
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…
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…
This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…
Stochastic simulators such as Monte-Carlo estimators are widely used in science and engineering to study physical systems through their probabilistic representation. Global sensitivity analysis aims to identify the input parameters which…
Global sensitivity analysis is the main quantitative technique for identifying the most influential input variables in a numerical simulation model. In particular when the inputs are independent, Sobol' sensitivity indices attribute a…
Integrating advanced communication protocols in production has accelerated the adoption of data-driven predictive quality methods, notably machine learning (ML) models. However, ML models in image classification often face significant…
This chapter makes a review, in a complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte…
A novel theoretical and numerical framework for the estimation of Sobol sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical…
The variance-based method of Sobol sensitivity indices is very popular among practitioners due to its efficiency and easiness of interpretation. However, for high-dimensional models the direct application of this method can be very time…
Sensitivity analysis (SA) is an important aspect of process automation. It often aims to identify the process inputs that influence the process output's variance significantly. Existing SA approaches typically consider the input-output…
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…
Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$…
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…
Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the…
In uncertainty quantification, evaluating sensitivity measures under specific conditions (i.e., conditional Sobol' indices) is essential for systems with parameterized responses, such as spatial fields or varying operating conditions.…
This study compares the performances of two sampling-based strategies for the simultaneous estimation of the first-and total-orders variance-based sensitivity indices (a.k.a Sobol' indices). The first strategy was introduced by [8] and is…