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For models evaluated at a random set of independent variables, the variance-based Shapley effects range between Sobol' indices, and the corresponding total indices admit derivative-based upper-bounds. Such relationships fail when the inputs…

Statistics Theory · Mathematics 2026-05-28 Matieyendou Lamboni

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…

Statistics Theory · Mathematics 2016-05-18 S. Kucherenko , O. V. Klymenko , N. Shah

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before…

Quantitative Methods · Quantitative Biology 2020-01-14 George Qian , Adam Mahdi

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…

Methodology · Statistics 2012-04-24 Art B. Owen

This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…

Numerical Analysis · Mathematics 2015-12-09 Sharif Rahman

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…

Statistics Theory · Mathematics 2021-01-15 Sébastien da Veiga

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.…

Statistics Theory · Mathematics 2021-01-21 Fabrice Gamboa , Thierry Klein , Agnès Lagnoux , Leonardo Moreno

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a…

Computation · Statistics 2021-06-01 X. Zhu , B. Sudret

Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular,…

Statistics Theory · Mathematics 2022-10-25 Julien Demange-Chryst , François Bachoc , Jérôme Morio

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…

Artificial Intelligence · Computer Science 2024-06-11 Rafael Ballester-Ripoll , Manuele Leonelli

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;…

Numerical Analysis · Mathematics 2016-07-28 Paul G. Constantine , Paul Diaz

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…

Numerical Analysis · Mathematics 2020-12-23 Chun Yui Wong , Pranay Seshadri , Geoffrey T. Parks

Factor importance measures the impact of each feature on output prediction accuracy. Many existing works focus on the model-based importance, but an important feature in one learning algorithm may hold little significance in another model.…

Methodology · Statistics 2025-06-24 Chaofan Huang , V. Roshan Joseph

Sensitivity analysis plays an important role in the development of computer models/simulators through identifying the contribution of each (uncertain) input factor to the model output variability. This report investigates different aspects…

Computation · Statistics 2022-06-24 Hossein Mohammadi , Peter Challenor , Clémentine Prieur

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.…

Statistics Theory · Mathematics 2026-03-03 Haythem Boucharif , Jérôme Morio , Paul Rochet

Models of complex technological systems inherently contain interactions and dependencies among their input variables that affect their joint influence on the output. Such models are often computationally expensive and few sensitivity…

Methodology · Statistics 2025-06-24 Mariia Kozlova , Antti Ahola , Pamphile T. Roy , Julian Scott Yeomans

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…

Methodology · Statistics 2013-05-13 Jean-Claude Fort , Thierry Klein , Nabil Rachdi

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…

Statistics Theory · Mathematics 2012-03-15 Sébastien Da Veiga , Fabrice Gamboa

Integrating advanced communication protocols in production has accelerated the adoption of data-driven predictive quality methods, notably machine learning (ML) models. However, ML models in image classification often face significant…

Machine Learning · Computer Science 2026-02-04 Lukas Bahr , Lucas Poßner , Konstantin Weise , Sophie Gröger , Rüdiger Daub

Code smells represent sub-optimal implementation choices applied by developers when evolving software systems. The negative impact of code smells has been widely investigated in the past: besides developers' productivity and ability to…

Software Engineering · Computer Science 2019-05-28 Gemma Catolino , Fabio Palomba , Francesca Arcelli Fontana , Andrea De Lucia , Andy Zaidman , Filomena Ferrucci