Related papers: Sensitivity indices for independent groups of vari…
We define and study a generalization of Sobol sensitivity indices for the case of a vector output.
In this paper we address the problem of efficient estimation of Sobol sensitivy indices. First, we focus on general functional integrals of conditional moments of the form $\E(\psi(\E(\varphi(Y)|X)))$ where $(X,Y)$ is a random vector with…
Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used…
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…
We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to…
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…
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…
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…
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…
Shapley effects are a particularly interpretable approach to assessing how a function depends on its various inputs. The existing literature contains various estimators for this class of sensitivity indices in the context of nonparametric…
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…
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…
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,…
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 $Y:=Y = f(X_1, \ldots, X_p)$…
This paper explores the application of active learning strategies to adaptively learn Sobol indices for global sensitivity analysis. We demonstrate that active learning for Sobol indices poses unique challenges due to the definition of the…
The main objective of this paper is to estimate optimally Sobol' indices at any order when a unique input/output i.i.d.\ sample is available. Our approach stands on three main ingredients: semi-parametric estimation theory, high-order…
In this paper, we introduce new indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called Sobol indices and the Cram{\'e}r-von-Mises indices.…
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…
Lower-dimensional subspaces that impact estimates of uncertainty are often described by Linear combinations of input variables, leading to active variables. This paper extends the derivative-based active subspace methods and…
In a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this…