相关论文: Sensitivity analysis for multidimensional and func…
Given a bivariate random pair $(X,Y)$, a natural problem is to estimate, from a single sample $(X_i,Y_i)_{1\le i\le n}$, quantities such as $\mathbb{E}\left[ \mathbb{E}[ Y\mid X ]^2 \right]$. More broadly, sensitivity indices are designed…
Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost;…
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…
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…
Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a…
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…
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…
Let $X$ be a (real or complex) rearrangement-in\-va\-riant function space on $\Om$ (where $\Om = [0,1]$ or $\Om \subseteq \bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize…
We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y . SIC decomposes to the sum of feature importance scores and hence can be used…
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,…
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…
ANOVA decomposition of function with random input variables provides ANOVA functionals (AFs), which contain information about the contributions of the input variables on the output variable(s). By embedding AFs into an appropriate…
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…
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…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
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 presents a simple noise correction method for Sobol' indices estimation. Sobol' indices, especially total Sobol' indices are quite sensitive to the noise in the output and tend to be severly biased (overestimated) if no noise…
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.…
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol' sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor…
In the past decade, Sobol's variance decomposition have been used as a tool - among others - in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of…