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We conduct the first comprehensive meta-analysis of deterministic solar forecasting based on skill score, screening 1,447 papers from Google Scholar and reviewing the full texts of 320 papers for data extraction. A database of 4,687 points…

Applications · Statistics 2023-04-13 Thi Ngoc Nguyen , Felix Müsgens

Despite the simplicity and intuitive interpretation of Minimum Mean Squared Error (MMSE) estimators, their effectiveness in certain scenarios is questionable. Indeed, minimizing squared errors on average does not provide any form of…

Optimization and Control · Mathematics 2019-12-09 Dionysios S. Kalogerias , Luiz F. O. Chamon , George J. Pappas , Alejandro Ribeiro

Forecasting entails a complex estimation challenge, as it requires balancing multiple, often conflicting, priorities and objectives. Traditional forecast optimization criteria typically focus on a single metric -- such as minimizing the…

Econometrics · Economics 2026-01-13 Marc Wildi

As regression is a widely studied problem, many methods have been proposed to solve it, each of them often requiring setting different hyper-parameters. Therefore, selecting the proper method for a given application may be very difficult…

Machine Learning · Computer Science 2026-03-23 Nassime Mountasir , Baptiste Lafabregue , Bruno Albert , Nicolas Lachiche

Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, such as the absolute error or the squared error. The individual scores are then averaged over forecast cases, to result in a…

Statistics Theory · Mathematics 2010-03-09 Tilmann Gneiting

What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…

Machine Learning · Computer Science 2024-10-31 Christian Fröhlich , Robert C. Williamson

Environmental model performances need to be assessed using some statistical parameters, such as mean absolute error (MAE) and root mean square error (RMSE). The advantages and disadvantages of these parameters are still in controversial.…

Applications · Statistics 2022-08-12 Weining Zhu

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most…

Statistics Theory · Mathematics 2022-03-29 David Bolin , Jonas Wallin

Traditional time series forecasting methods optimize for accuracy alone. This objective neglects temporal consistency, in other words, how consistently a model predicts the same future event as the forecast origin changes. We introduce the…

Machine Learning · Computer Science 2026-04-24 Chutian Ma , Grigorii Pomazkin , Giacinto Paolo Saggese , Paul Smith

Modern weather forecasting has increasingly transitioned from numerical weather prediction (NWP) to data-driven machine learning forecasting techniques. While these new models produce probabilistic forecasts to quantify uncertainty, their…

Machine Learning · Statistics 2026-05-01 Archer Dodson , Ritabrata Dutta

This paper describes the RRMSE (Relative Root Mean Square Error) based weights to weight the occurrences of predictive values before averaging for the ensemble voting regression. The core idea behind ensemble regression is to combine…

Machine Learning · Computer Science 2022-07-12 Shikun Chen , Nguyen Manh Luc

Improvement of the prediction accuracy of the Earth's rotation parameters (ERP) is one of the main problems of applied astrometry. In order to solve this problem, various approaches are used and in order to select the best one, comparison…

Geophysics · Physics 2023-04-11 Z. M. Malkin , V. M. Tissen

The construction of computer models (mathematical models implemented in computer codes), with respect to observed phenomena, is usually undertaken by building different variants depending on modeller sensibility, and choosing the one…

Methodology · Statistics 2018-03-28 Filippo Monari

Root-mean-square error (RMSE) remains the default training loss for data-driven precipitation models, despite precipitation being semi-continuous, zero-inflated, strictly non-negative, and heavy-tailed. This Gaussian-implied objective…

Atmospheric and Oceanic Physics · Physics 2025-09-11 Kieran M. R. Hunt

Meaningful scores for forecast verification are essential for developing reliable forecasts, and there has been much effort to develop scores that align well with human perceptions of forecast quality. Whilst many of these scores have…

Atmospheric and Oceanic Physics · Physics 2026-03-17 Bobby Antonio

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good…

Machine Learning · Computer Science 2023-06-07 Étienne Marcotte , Valentina Zantedeschi , Alexandre Drouin , Nicolas Chapados

This work presents a set of optimal machine learning (ML) models to represent the temporal degradation suffered by the power conversion efficiency (PCE) of polymeric organic solar cells (OSCs) with a multilayer structure…

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean…

Machine Learning · Statistics 2017-03-16 Johan Wågberg , Dave Zachariah , Thomas B. Schön , Petre Stoica

This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…

Information Theory · Computer Science 2019-09-04 Alex Dytso , Martina Cardone , H. Vincent Poor

The Fractions Skill Score (FSS) is a widely used metric for assessing forecast skill, with applications ranging from precipitation to volcanic ash forecasts. By evaluating the fraction of grid squares exceeding a threshold in a…

Atmospheric and Oceanic Physics · Physics 2026-05-28 Bobby Antonio , Laurence Aitchison
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