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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

Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…

Computational Engineering, Finance, and Science · Computer Science 2019-09-05 Alexander Tarakanov , Ahmed H. Elsheikh

Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…

Numerical Analysis · Mathematics 2017-09-27 Melvin Leok , Gautam Wilkins

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…

Probability · Mathematics 2015-06-22 Jerrad Hampton , Alireza Doostan

The method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them.…

Statistics Theory · Mathematics 2023-12-05 Serge Kucherenko , Bertrand Iooss

Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have…

Computational Engineering, Finance, and Science · Computer Science 2023-01-10 Barbara Wirthl , Sebastian Brandstaeter , Jonas Nitzler , Bernhard A. Schrefler , Wolfgang A. Wall

Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…

Methodology · Statistics 2023-06-02 Juraj Kardos , Wouter Edeling , Diana Suleimenova , Derek Groen , Olaf Schenk

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many…

Methodology · Statistics 2024-06-19 Joy N. Mueller , Khachik Sargsyan , Craig J. Daniels , Habib N. Najm

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary…

Probability · Mathematics 2017-05-17 Katia Bachi , Cédric Chauvière , Hacène Djellout , Karim Abbas

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…

Statistics Theory · Mathematics 2013-06-03 Loic Le Gratiet

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…

Statistics Theory · Mathematics 2020-01-22 Viet Chi Tran , Gwenaëlle Castellan , Anthony Cousien , Chi Tran

Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…

Computation · Statistics 2012-11-13 Lorenzo Fagiano , Mustafa Khammash

We propose a new statistical estimation framework for a large family of global sensitivity analysis methods. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee. We…

Statistics Theory · Mathematics 2023-06-29 Fabrice Gamboa , Pierre Gremaud , Thierry Klein , Agnès Lagnoux

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

Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully…

Methodology · Statistics 2025-10-30 Kellin N. Rumsey , Devin Francom , Graham C. Gibson , J. Derek Tucker , Gabriel Huerta

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

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…

Statistics Theory · Mathematics 2025-03-25 Robert A. Milton , Solomon F. Brown

Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse…

Data Analysis, Statistics and Probability · Physics 2019-11-01 Nando Farchmin , Martin Hammerschmidt , Philipp-Immanuel Schneider , Matthias Wurm , Bernd Bodermann , Markus Bär , Sebastian Heidenreich

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

Numerical Analysis · Mathematics 2018-11-28 Xiu Yang , Xiaoliang Wan , Lin Lin , Huan Lei

A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…

Numerical Analysis · Mathematics 2019-11-12 Sharif Rahman