Related papers: Variance components and generalized Sobol' indices
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…
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…
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…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
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…
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…
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…
Sobol' indices measure the dependence of a high dimensional function on groups of variables defined on the unit cube $[0,1]^d$. They are based on the ANOVA decomposition of functions, which is an $L^2$ decomposition. In this paper we…
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…
We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…
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…
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.…
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 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…
Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing…
Global sensitivity analysis aims at quantifying respective effects of input random variables (or combinations thereof) onto variance of a physical or mathematical model response. Among the abundant literature on sensitivity measures, Sobol'…
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…
Among the many estimators of first order Sobol indices that have been proposed in the literature, the so-called rank-based estimator is arguably the simplest to implement. This estimator can be viewed as the empirical auto-correlation of…
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…
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…