相关论文: Sensitivity analysis for multidimensional and func…
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…
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…
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…
The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when…
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…
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…
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.…
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…
This article investigates a new procedure to estimate the influence of each variable of a given function defined on a high-dimensional space. More precisely, we are concerned with describing a function of a large number $p$ of parameters…
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…
We define and study a generalization of Sobol sensitivity indices for the case of a vector output.
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' 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…
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…
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 this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a…
Sensitivity indices are commonly used to quantify the relative influence of any specific group of input variables on the output of a computer code. One crucial question is then to decide whether a given set of variables has a significant…
Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…
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…
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…