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Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…

Probability · Mathematics 2015-07-15 Paul Dupuis , Markos A. Katsoulakis , Yannis Pantazis , Petr Plechac

In this letter, we analytically investigate the sensitivity of stability index to its dependent variables in general power systems. Firstly, we give a small-signal model, the stability index is defined as the solution to a semidefinite…

Optimization and Control · Mathematics 2023-01-27 Jun Wang , Yue Song , David John Hill , Yunhe Hou

We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee [9]. We…

Methodology · Statistics 2026-05-25 Fabrice Gamboa , Pierre Gremaud , Thierry Klein , Agnès Lagnoux

The main objective of this paper is to propose a new approach for estimating the entire collection of Sobol' indices simultaneously. Our approach exploits the fact that Sobol' indices can be rewritten as solutions to an optimization problem…

Statistics Theory · Mathematics 2025-12-09 Manon Costa , Sébastien Gadat , Xavier Gendre , Thierry Klein

There are strong incentives to build models that demonstrate outstanding predictive performance on various datasets and benchmarks. We believe these incentives risk a narrow focus on models and on the performance metrics used to evaluate…

Machine Learning · Computer Science 2022-06-07 David Lovell , Dimity Miller , Jaiden Capra , Andrew Bradley

Output uncertainty indicates whether the probabilistic properties reflect objective characteristics of the model output. Unlike most loss functions and metrics in machine learning, uncertainty pertains to individual samples, but validating…

Machine Learning · Computer Science 2024-12-23 Siyuan Zhang , Linbo Xie

In this paper, we first study a new sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo ([3]), we define and study a new sensitivity index based on the…

Probability · Mathematics 2017-12-01 Fabrice Gamboa , Thierry Klein , Agnès Lagnoux

Modern data-driven applications that make real-time decisions increasingly depend on advanced sensors which use pre-stored calibration data. In such applications, accurate characterization of sensor output uncertainty is important for…

Signal Processing · Electrical Eng. & Systems 2026-03-09 Orestis Kaparounakis , Phillip Stanley-Marbell

In this paper we apply a methodology introduced in Navarro Jimenez et al (2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by…

Methodology · Statistics 2024-07-26 Henri Mermoz Kouye , Gildas Mazo , Clémentine Prieur , Elisabeta Vergu

Sensitivity analysis helps identify which model inputs convey the most uncertainty to the model output. One of the most authoritative measures in global sensitivity analysis is the Sobol' total-order index, which can be computed with…

Applications · Statistics 2021-07-30 Arnald Puy , William Becker , Samuele Lo Piano , Andrea Saltelli

In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs.…

Statistics Theory · Mathematics 2022-09-12 Matieyendou Lamboni

Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions…

Systems and Control · Electrical Eng. & Systems 2021-10-28 Shengling Shi , Xiaodong Cheng , Paul M. J. Van den Hof

Identifiability concerns finding which unknown parameters of a model can be estimated from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is…

Algebraic Geometry · Mathematics 2014-11-03 Nicolette Meshkat , Seth Sullivant , Marisa Eisenberg

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…

Machine Learning · Computer Science 2025-10-30 Christopher Bülte , Yusuf Sale , Gitta Kutyniok , Eyke Hüllermeier

In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases,…

Statistical Mechanics · Physics 2019-07-17 Benjamin L. Francis , Mark K. Transtrum

Time series anomaly detection is widely used in IoT and cyber-physical systems, yet its evaluation remains challenging due to diverse application objectives and heterogeneous metric assumptions. This study introduces a problem-oriented…

Artificial Intelligence · Computer Science 2026-05-15 Kaixiang Yang , Jiarong Liu , Yupeng Song , Shuanghua Yang , Yujue Zhou

An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are…

Physics and Society · Physics 2017-08-23 Yueying Zhu , Qiuping A Wang , Wei Li , Xu Cai

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Machine Learning · Statistics 2023-03-15 Hengrui Luo , Justin D. Strait

Causal inference with observational studies often suffers from unmeasured confounding, yielding biased estimators based on the unconfoundedness assumption. Sensitivity analysis assesses how the causal conclusions change with respect to…

Methodology · Statistics 2024-04-01 Sizhu Lu , Peng Ding

Sensitivity analysis is a process of computing sensitivity indices, which are certain measures of importance of parameters in influencing the outputs of mathematical models. Sensitivity indices computed in variance-based sensitivity…

Computation · Statistics 2013-10-04 Tomasz Badowski