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This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

Statistical Mechanics · Physics 2025-08-19 Marco Biroli

Nowadays, the numerical models of real-world structures are more precise, more complex and, of course, more time-consuming. Despite the growth of a computational effort, the exploration of model behaviour remains a complex task. The…

Computational Engineering, Finance, and Science · Computer Science 2014-10-17 Eliska Janouchova , Anna Kucerova

Identifying causal treatment (or exposure) effects in observational studies requires the data to satisfy the unconfoundedness assumption which is not testable using the observed data. With sensitivity analysis, one can determine how the…

Methodology · Statistics 2023-01-31 Yang Ou , Lu Tang , Chung-Chou H. Chang

Sensitivity analysis is widely used to assess the robustness of causal conclusions in observational studies, yet its interaction with the structure of measured covariates is often overlooked. When latent confounders cannot be directly…

Methodology · Statistics 2026-02-17 Abhinandan Dalal , Iris Horng , Yang Feng , Dylan S. Small

The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological…

Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…

Artificial Intelligence · Computer Science 2012-07-09 Silja Renooij , Linda C. van der Gaag

Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a…

Quantitative Methods · Quantitative Biology 2007-12-04 Zhihui Wang , Christina M. Birch , Thomas S. Deisboeck

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

Our article considers a regression model with observed factors. The observed factors have a flexible stochastic volatility structure that has separate dynamics for the volatilities and the correlation matrix. The correlation matrix of the…

Other Statistics · Statistics 2011-07-14 Yu-Cheng Ku , Peter Bloomfield , Robert Kohn

With the advance of efficient analytical methods for sensitivity analysis ofprobabilistic networks, the interest in the sensitivities revealed by real-life networks is rekindled. As the amount of data resulting from a sensitivity analysis…

Artificial Intelligence · Computer Science 2013-01-14 Linda C. van der Gaag , Silja Renooij

The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…

Machine Learning · Statistics 2018-10-01 Christiane Goergen , Manuele Leonelli

This work undertakes studies to evaluate Interpretability Methods for Time-Series Deep Learning. Sensitivity analysis assesses how input changes affect the output, constituting a key component of interpretation. Among the post-hoc…

Machine Learning · Computer Science 2024-01-31 Zhengguang Wang

The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…

Statistics Theory · Mathematics 2019-11-26 Bertrand Iooss , Clémentine Prieur

Causal Machine Learning has emerged as a powerful tool for flexibly estimating causal effects from observational data in both industry and academia. However, causal inference from observational data relies on untestable assumptions about…

We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…

Probability · Mathematics 2014-04-18 Ankit Gupta , Mustafa Khammash

Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we…

Statistics Theory · Mathematics 2013-11-12 Sébastien Da Veiga

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

Variable importance, interaction measures, and partial dependence plots are important summaries in the interpretation of statistical and machine learning models. In this paper we describe new visualization techniques for exploring these…

Computation · Statistics 2021-10-12 Alan Inglis , Andrew Parnell , Catherine Hurley

In this paper, we present perturbed law-based sensitivity indices and how to adapt them for quantile-oriented sensitivity analysis. We exhibit a simple way to compute these indices in practice using an importance sampling estimator for…

Statistics Theory · Mathematics 2017-07-06 Roman Sueur , Bertrand Iooss , Thibault Delage

Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation…