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Probabilistic prediction of stochastic dynamical systems (SDSs) aims to accurately predict the conditional probability distributions of future states. However, accurate probabilistic predictions tightly hinge on accurate distributional…

Optimization and Control · Mathematics 2026-04-21 Tao Xu , Jianping He

In this paper, we predict severity of extreme weather events (tropical storms, hurricanes, etc.) using buoy data time series variables such as wind speed and air temperature. The prediction/forecasting method is based on various forecasting…

Applications · Statistics 2019-11-21 Vikas Ramachandra

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the…

Machine Learning · Computer Science 2024-10-29 Joel Oskarsson , Tomas Landelius , Marc Peter Deisenroth , Fredrik Lindsten

The theoretical advances on the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to…

Statistics Theory · Mathematics 2022-12-13 Romain Pic , Clément Dombry , Philippe Naveau , Maxime Taillardat

Accurately representing surface weather at the sub-kilometer scale is crucial for optimal decision-making in a wide range of applications. This motivates the use of statistical techniques to provide accurate and calibrated probabilistic…

Atmospheric and Oceanic Physics · Physics 2024-11-15 Francesco Zanetta , Daniele Nerini , Matteo Buzzi , Henry Moss

Probabilistic forecasting relies on past observations to provide a probability distribution for a future outcome, which is often evaluated against the realization using a scoring rule. Here, we perform probabilistic forecasting with…

Machine Learning · Statistics 2024-03-06 Lorenzo Pacchiardi , Rilwan Adewoyin , Peter Dueben , Ritabrata Dutta

With increasing concerns of climate change, renewable resources such as photovoltaic (PV) have gained popularity as a means of energy generation. The smooth integration of such resources in power system operations is enabled by accurate…

Applications · Statistics 2021-03-30 Fatemeh Najibi , Dimitra Apostolopoulou , Eduardo Alonso

Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a difficult…

Methodology · Statistics 2023-01-05 Yuanlu Bai , Henry Lam , Xinyu Zhang

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…

Machine Learning · Statistics 2024-03-19 Hristos Tyralis , Georgia Papacharalampous

In this work, we investigate the reliability of the probabilistic binary forecast. We mathematically prove that a necessary, but not sufficient, condition for achieving a reliable probabilistic forecast is maximizing the Peirce skill score…

Space Physics · Physics 2019-05-20 Yûki Kubo

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

A new method is proposed for modelling the yearly maxima of sub-daily precipitation, with the aim of producing spatial maps of return level estimates. Yearly precipitation maxima are modelled using a Bayesian hierarchical model with a…

Applications · Statistics 2022-09-23 Silius M. Vandeskog , Sara Martino , Daniela Castro-Camilo , Håvard Rue

The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…

Applications · Statistics 2022-10-06 Jethro Browell , Matteo Fasiolo

We quantify changes DeltaQ in 100-year return values for regional annual maxima and minima of near-surface atmospheric temperature from output of five CMIP6 models, for five of the Earth's desert regions, over the interval (2025,2125). We…

Atmospheric and Oceanic Physics · Physics 2026-03-16 Callum Leach , Kevin Ewans , Philip Jonathan

Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way…

Statistical Mechanics · Physics 2015-05-21 Satya N. Majumdar , Arnab Pal

Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…

Applications · Statistics 2022-05-24 Naoufal Acharki , Antoine Bertoncello , Josselin Garnier

This paper explores the implications of producing forecast distributions that are optimized according to scoring rules that are relevant to financial risk management. We assess the predictive performance of optimal forecasts from…

Statistical Finance · Quantitative Finance 2023-03-06 Yuru Sun , Worapree Maneesoonthorn , Ruben Loaiza-Maya , Gael M. Martin

Weather forecasting requires not only accuracy but also the ability to perform probabilistic prediction. However, deterministic weather forecasting methods do not support probabilistic predictions, and conversely, probabilistic models tend…

Computer Vision and Pattern Recognition · Computer Science 2023-12-06 Donggeun Yoon , Minseok Seo , Doyi Kim , Yeji Choi , Donghyeon Cho

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated…

Statistical Mechanics · Physics 2022-08-29 Lior Zarfaty , Eli Barkai , David A. Kessler

Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…

Optimization and Control · Mathematics 2014-07-09 Eric Dow , Qiqi Wang