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The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves)…

Chemical Physics · Physics 2023-03-31 Pascal Pernot

The purpose of this study is to perform verification of the structural characteristics of high-resolution spatial forecasts without relying on an object identification algorithm. To this end, a wavelet approach developed for image texture…

Applications · Statistics 2018-08-24 Florian Kapp , Petra Friederichs , Sebastian Brune , Michael Weniger

Prior to clinical applications, it is critical that risk prediction models are evaluated in independent studies that did not contribute to model development. While prospective cohort studies provide a natural setting for model validation,…

Methodology · Statistics 2017-10-13 Parichoy Pal Choudhury , Anil K. Chaturvedi , Nilanjan Chatterjee

This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for…

Quantum Physics · Physics 2026-03-30 Ryan Bennink , Olena Burkovska , Konstantin Pieper , Jorge Ramirez , Elaine Wong

Artificial intelligence (AI)-based data-driven weather forecasting models have experienced rapid progress over the last years. Recent studies, with models trained on reanalysis data, achieve impressive results and demonstrate substantial…

Atmospheric and Oceanic Physics · Physics 2025-04-02 Christopher Bülte , Nina Horat , Julian Quinting , Sebastian Lerch

We focus on the time-varying modeling of VaR at a given coverage $\tau$, assessing whether the quantiles of the distribution of the returns standardized by their conditional means and standard deviations exhibit predictable dynamics. Models…

Risk Management · Quantitative Finance 2023-06-01 Fabrizio Cipollini , Giampiero M. Gallo , Alessandro Palandri

With the growing number of forecasting techniques and the increasing significance of forecast-based operation - particularly in the rapidly evolving energy sector - selecting the most effective forecasting model has become a critical task.…

Systems and Control · Electrical Eng. & Systems 2024-10-24 Fabian Backhaus , Karoline Brucke , Peter Ruckdeschel , Sunke Schlüters

Delivering precise point and distributional forecasts across a spectrum of prediction horizons represents a significant and enduring challenge in the application of time-series forecasting within various industries. Prior research on…

Machine Learning · Computer Science 2024-10-22 Jiawen Zhang , Xumeng Wen , Zhenwei Zhang , Shun Zheng , Jia Li , Jiang Bian

Conformal prediction is a powerful framework for distribution-free uncertainty quantification. The standard approach to conformal prediction relies on comparing the ranks of prediction scores: under exchangeability, the rank of a future…

Machine Learning · Statistics 2025-05-07 Etienne Gauthier , Francis Bach , Michael I. Jordan

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…

Machine Learning · Statistics 2023-04-18 Rasool Fakoor , Taesup Kim , Jonas Mueller , Alexander J. Smola , Ryan J. Tibshirani

Rotating machinery is essential to modern life, from power generation to transportation and a host of other industrial applications. Since such equipment generally operates under challenging working conditions, which can lead to untimely…

Signal Processing · Electrical Eng. & Systems 2021-09-27 Zhaoyi Xu , Yanjie Guo , Joseph Homer Saleh

Interest has been growing in decision-focused machine learning methods which train models to account for how their predictions are used in downstream optimization problems. Doing so can often improve performance on subsequent decision…

Machine Learning · Computer Science 2025-03-03 Santiago Cortes-Gomez , Carlos Patiño , Yewon Byun , Steven Wu , Eric Horvitz , Bryan Wilder

The ROC curve is widely used to assess the quality of prediction/classification/ranking algorithms, and its properties have been extensively studied. The precision-recall (PR) curve has become the de facto replacement for the ROC curve in…

Machine Learning · Statistics 2018-10-23 Jacqueline M. Hughes-Oliver

The receiver operating characteristic (ROC) curve is a very useful tool for analyzing the diagnostic/classification power of instruments/classification schemes as long as a binary-scale gold standard is available. When the gold standard is…

Methodology · Statistics 2011-05-10 Zhanfeng Wang , Yuan-chin Ivan Chang

Scoring functions are used to evaluate and compare partially probabilistic forecasts. We investigate the use of rank-sum functions such as empirical Area Under the Curve (AUC), a widely-used measure of classification performance, as a…

Statistics Theory · Mathematics 2017-01-31 Simon Byrne

The recent developments in the machine learning domain have enabled the development of complex multivariate probabilistic forecasting models. Therefore, it is pivotal to have a precise evaluation method to gauge the performance and…

Machine Learning · Computer Science 2023-02-01 Alireza Koochali , Peter Schichtel , Andreas Dengel , Sheraz Ahmed

As the world increasingly relies on mathematical models for forecasts in different areas, effective communication of uncertainty in time series predictions is important for informed decision making. This study explores how users estimate…

Human-Computer Interaction · Computer Science 2024-08-23 Apoorva Karagappa , Pawandeep Kaur Betz , Jonas Gilg , Moritz Zeumer , Andreas Gerndt , Bernhard Preim

Quantile regression, the prediction of conditional quantiles, finds applications in various fields. Often, some or all of the variables are discrete. The authors propose two new quantile regression approaches to handle such mixed…

Methodology · Statistics 2017-05-24 Niklas Schallhorn , Daniel Kraus , Thomas Nagler , Claudia Czado

Quantifying the uncertainty of forecasting models is essential to assess and mitigate the risks associated with data-driven decisions, especially in volatile domains such as electricity markets. Machine learning methods can provide highly…

Machine Learning · Computer Science 2025-07-22 Arkadiusz Lipiecki , Bartosz Uniejewski

Any decision making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This paper proposes new methods for empirically assessing forecast calibration in a multivariate setting where…

Methodology · Statistics 2014-07-02 Thordis L. Thorarinsdottir , Michael Scheuerer , Christopher Heinz