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Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models; to estimate model errors and thereby improve predictive capability; to…

Nuclear Theory · Physics 2015-03-26 J. D. McDonnell , N. Schunck , D. Higdon , J. Sarich , S. M. Wild , W. Nazarewicz

The idea to distinguish and quantify two important types of uncertainty, often referred to as aleatoric and epistemic, has received increasing attention in machine learning research in the last couple of years. In this paper, we consider…

Machine Learning · Computer Science 2021-12-13 Mohammad Hossein Shaker , Eyke Hüllermeier

Atmospheric aerosols influence the Earth's climate, primarily by affecting cloud formation and scattering visible radiation. However, aerosol-related physical processes in climate simulations are highly uncertain. Constraining these…

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…

Integrated Assessment Models (IAMs) are pivotal tools that synthesize knowledge from climate science, economics, and policy to evaluate the interactions between human activities and the climate system. They serve as essential instruments…

General Economics · Economics 2025-11-04 Yongyang Cai

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

Machine Learning · Computer Science 2024-01-02 Yusuf Sale , Paul Hofman , Lisa Wimmer , Eyke Hüllermeier , Thomas Nagler

The calibration of predictive distributions has been widely studied in deep learning, but the same cannot be said about the more specific epistemic uncertainty as produced by Deep Ensembles, Bayesian Deep Networks, or Evidential Deep…

Machine Learning · Computer Science 2024-07-18 Mohammed Fellaji , Frédéric Pennerath , Brieuc Conan-Guez , Miguel Couceiro

Practitioners making decisions based on causal effects typically ignore structural uncertainty. We analyze when this uncertainty is consequential enough to warrant methodological solutions (Bayesian model averaging over competing causal…

Machine Learning · Computer Science 2025-08-01 Maurits Kaptein

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Machine Learning · Computer Science 2023-11-09 Vardhan Dongre , Gurpreet Singh Hora

In this work, we introduce Entropy Area Score (EAS), a simple yet effective metric to quantify uncertainty in the answer generation process of reasoning large language models (LLMs). EAS requires neither external models nor repeated…

Artificial Intelligence · Computer Science 2025-08-29 Yongfu Zhu , Lin Sun , Guangxiang Zhao , Weihong Lin , Xiangzheng Zhang

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

Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…

Machine Learning · Computer Science 2022-11-14 Levente Foldesi , Matias Valdenegro-Toro

Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…

Methodology · Statistics 2025-04-01 Carlos García Meixide , Michael R. Kosorok , Marcos Matabuena

Modern Large Language Models (LLMs) often require external tools, such as machine learning classifiers or knowledge retrieval systems, to provide accurate answers in domains where their pre-trained knowledge is insufficient. This…

Machine Learning · Computer Science 2025-05-23 Panagiotis Lymperopoulos , Vasanth Sarathy

Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…

Methodology · Statistics 2026-03-18 Oliver L. Pescott , Robin J. Boyd , Gary D. Powney , Gavin B. Stewart

Uncertainty quantification (UQ) is essential for assessing the reliability of Earth observation (EO) products. However, the extensive use of machine learning models in EO introduces an additional layer of complexity, as those models…

Machine Learning · Computer Science 2024-12-10 Yuanyuan Wang , Qian Song , Dawood Wasif , Muhammad Shahzad , Christoph Koller , Jonathan Bamber , Xiao Xiang Zhu

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Machine Learning · Computer Science 2023-06-27 Lisa Wimmer , Yusuf Sale , Paul Hofman , Bern Bischl , Eyke Hüllermeier

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the…

Machine Learning · Computer Science 2023-04-14 Marco Forgione , Dario Piga

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…

High Energy Physics - Theory · Physics 2016-03-17 Pedro R. S. Gomes

Economic assessment in environmental science concerns the measurement or valuation of environmental impacts, adaptation, and vulnerability. Integrated assessment modeling is a unifying framework of environmental economics, which attempts to…

General Economics · Economics 2020-09-02 Ruda Zhang , Patrick Wingo , Rodrigo Duran , Kelly Rose , Jennifer Bauer , Roger Ghanem