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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…

Machine Learning · Statistics 2021-10-11 Rafael Ballester-Ripoll , Manuele Leonelli

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…

Data Analysis, Statistics and Probability · Physics 2018-08-17 Joseph Hart , Pierre Gremaud

We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semi-parametric approach and represent the interaction kernel in terms of a…

Statistics Theory · Mathematics 2025-10-31 Grigorios A. Pavliotis , Andrea Zanoni

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'…

Computation · Statistics 2017-05-12 E. Burnaev , I. Panin , B. Sudret

A variety of indices aim to quantify the impact of input variables on a response, typically the output from a complex computer code or black-box model. Most commonly used, the Sobol' index typically measures the influence of some inputs…

Statistics Theory · Mathematics 2025-07-22 Thierry Klein , Agnès Lagnoux , Paul Rochet , Thi Mong Ngoc Nguyen

The level dependent Choquet integral has been proposed to handle decision making problems in which the importance and the interaction of criteria may depend on the level of the alternatives' evaluations. This integral is based on a level…

Optimization and Control · Mathematics 2019-05-21 Sally Giuseppe Arcidiacono , Salvatore Corrente , Salvatore Greco

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…

Numerical Analysis · Mathematics 2016-06-03 Sergei Kucherenko , Shufang Song

The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…

Functional Analysis · Mathematics 2025-05-06 Sarga Varghese , Gita Rani Mahato , Manab Kundu

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…

Numerical Analysis · Computer Science 2017-12-04 Rafael Ballester-Ripoll , Enrique G. Paredes , Renato Pajarola

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…

Computation · Statistics 2016-05-31 K. Konakli , B. Sudret

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…

Machine Learning · Statistics 2025-09-16 Teresa Portone , Bert Debusschere , Samantha Yang , Emiliano Islas-Quinones , T. Patrick Xiao

In this paper we propose a new multiple criteria decision aiding method to deal with sorting problems in which alternatives are evaluated on criteria structured in a hierarchical way and presenting interactions. The underlying preference…

Optimization and Control · Mathematics 2020-03-11 Sally Giuseppe Arcidiacono , Salvatore Corrente , Salvatore Greco

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…

Statistics Theory · Mathematics 2013-03-26 Alexandre Janon

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…

Methodology · Statistics 2024-08-12 Thomas Most

In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral.…

Functional Analysis · Mathematics 2016-11-11 Salvatore Greco , Fabio Rindone

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…

Statistics Theory · Mathematics 2022-04-05 Thierry Klein , Nicolas Peteilh , Paul Rochet

In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…

Combinatorics · Mathematics 2025-04-29 László Lovász

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…

Statistics Theory · Mathematics 2014-07-22 Areski Cousin , Alexandre Janon , Véronique Maume-Deschamps , Ibrahima Niang

In this paper we address the problem of fuzzy measures index calculation. On the basis of fuzzy sets, Murofushi and Soneda proposed an interaction index to deal with the relations between two individuals. This index was later extended in a…

Statistics Theory · Mathematics 2024-02-08 Inmaculada Gutiérrez , Javier Castro , Daniel Gómez , Rosa Espínola

The Lovasz extension of a pseudo-Boolean function $f : \{0,1\}^n \to R$ is defined on each simplex of the standard triangulation of $[0,1]^n$ as the unique affine function $\hat f : [0,1]^n \to R$ that interpolates $f$ at the $n+1$ vertices…

Combinatorics · Mathematics 2010-11-19 Jean-Luc Marichal , Pierre Mathonet