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Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere, necessitating probabilistic approaches to quantify uncertainty. While traditional ensemble prediction (EPS) addresses this through computationally…

Machine Learning · Computer Science 2025-11-19 Xinlei Xiong , Wenbo Hu , Shuxun Zhou , Kaifeng Bi , Lingxi Xie , Ying Liu , Richang Hong , Qi Tian

We derive the general analytical expressions for the statistical uncertainties of cumulants up to fourth order including an efficiency correction. The analytical expressions have been tested with a toy Monte Carlo model analysis. An…

Nuclear Theory · Physics 2022-03-25 Fan Si , Yifei Zhang

Coastal flooding drives considerable risks to many communities, but projections of future flood risks are deeply uncertain. The paucity of observations of extreme events often motivates the use of statistical approaches to model the…

Applications · Statistics 2018-08-01 Tony E. Wong , Alexandra Klufas , Vivek Srikrishnan , Klaus Keller

Efficiently and meaningfully estimating prediction uncertainty is important for exploration in active learning campaigns in materials discovery, where samples with high uncertainty are interpreted as containing information missing from the…

Materials Science · Physics 2025-11-25 Ashley S. Dale , Kangming Li , Brian DeCost , Hao Wan , Yuchen Han , Yao Fehlis , Jason Hattrick-Simpers

Extreme events, such as wave-storms, need to be characterized for coastal infrastructure design purposes. Such description should contain information on both the univariate behaviour and the joint-dependence of storm-variables. These two…

Atmospheric and Oceanic Physics · Physics 2019-03-15 Jue Lin-Ye , Manuel García-León , Vicente Gràcia , Maribel Ortego , Piero Lionello , Agustín Sanchez-Arcilla

Accurate prediction of extreme weather events remains a major challenge for artificial intelligence-based weather prediction systems. While deterministic models such as FuXi, GraphCast, and SFNO have achieved competitive forecast skill…

Atmospheric and Oceanic Physics · Physics 2026-05-01 Rodrigo Almeida , Noelia Otero , Miguel-Ángel Fernández-Torres , Jackie Ma

This paper provides a simple, yet reliable, alternative to the (Bayesian) estimation of large multivariate VARs with time variation in the conditional mean equations and/or in the covariance structure. With our new methodology, the original…

Econometrics · Economics 2020-01-01 Mike Tsionas , Marwan Izzeldin , Lorenzo Trapani

The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties,…

Nuclear Theory · Physics 2018-12-10 Sota Yoshida , Noritaka Shimizu , Tomoaki Togashi , Takaharu Otsuka

Skill scores, which measure the relative improvement of a forecasting method over a benchmark via consistent scoring functions and proper scoring rules, are a standard tool in forecast evaluation, yet their sampling uncertainty is rarely…

Methodology · Statistics 2026-05-06 Marc-Oliver Pohle , Tanja Zahn , Sebastian Lerch

In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed "event attribution." Limitations in the observational record and in…

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

Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…

Applications · Statistics 2016-05-25 Stefan Siegert , Philip G. Sansom , Robin Williams

Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…

Applications · Statistics 2019-07-05 Ali Reza Fotouhi

Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…

Dynamical Systems · Mathematics 2026-03-25 Mohamed Akrout , Dan Wilson

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…

Computer Vision and Pattern Recognition · Computer Science 2024-05-14 Omer Yair , Elias Nehme , Tomer Michaeli

The paper introduces a new regression model designed for situations where both the response and covariates are non-stationary extremes. This method is specifically designed for situations where both the response variable and covariates are…

Methodology · Statistics 2025-06-26 Amina El Bernoussi , Mohamed El Arrouchi

Uncertainties from model parameters and model discrepancy from small-scale models impact the accuracy and reliability of predictions of large-scale systems. Inadequate representation of these uncertainties may result in inaccurate and…

Methodology · Statistics 2014-12-18 K. Sham Bhat , David S. Mebane , Curtis B. Storlie , Priyadarshi Mahapatra

Robust quantification of predictive uncertainty is critical for understanding factors that drive weather and climate outcomes. Ensembles provide predictive uncertainty estimates and can be decomposed physically, but both physics and machine…

The interdependence of electricity and natural gas markets is becoming a major topic in energy research. Integrated energy models are used to assist decision-making for businesses and policymakers addressing challenges of energy transition…

General Finance · Quantitative Finance 2020-09-11 Iegor Riepin , Thomas Möbius , Felix Müsgens

Future greenhouse gas neutral energy systems will be dominated by renewable energy technologies providing variable supply subject to uncertain weather conditions. For this setting, we propose an algorithm for capacity expansion planning: We…

Optimization and Control · Mathematics 2026-03-02 Sebastian Kebrich , Felix Engelhardt , David Franzmann , Christina Büsing , Jochen Linßen , Heidi Heinrichs
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