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The continuous ranked probability score (crps) is the most commonly used scoring rule in the evaluation of probabilistic forecasts for real-valued outcomes. To assess and rank forecasting methods, researchers compute the mean crps over…

Methodology · Statistics 2023-11-27 Sebastian Arnold , Eva-Maria Walz , Johanna Ziegel , Tilmann Gneiting

Rare weather and climate events, such as heat waves and floods, can bring tremendous social costs. Climate data is often limited in duration and spatial coverage, and climate forecasting has often turned to simulations of climate models to…

Methodology · Statistics 2020-05-18 Meagan Carney , Holger Kantz , Matthew Nicol

The evaluation of probabilistic forecasts plays a central role both in the interpretation and in the use of forecast systems and their development. Probabilistic scores (scoring rules) provide statistical measures to assess the quality of…

Methodology · Statistics 2020-12-24 Hailiang Du

This paper proposes a novel asymmetric continuous probabilistic score (ACPS) for evaluating and comparing density forecasts. It extends the proposed score and defines a weighted version, which emphasizes regions of interest, such as the…

Methodology · Statistics 2020-09-02 Matteo Iacopini , Francesco Ravazzolo , Luca Rossini

Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value…

Methodology · Statistics 2019-03-06 Jasper Velthoen , Juan-Juan Cai , Geurt Jongbloed , Maurice Schmeits

To mitigate the impacts associated with adverse weather conditions, meteorological services issue weather warnings to the general public. These warnings rely heavily on forecasts issued by underlying prediction systems. When deciding which…

Applications · Statistics 2022-09-13 Sam Allen , Jonas Bhend , Olivia Martius , Johanna Ziegel

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

Methodology · Statistics 2015-05-28 Ville Satopää , Robin Pemantle , Lyle Ungar

Event attribution in the context of climate change seeks to understand the role of anthropogenic greenhouse gas emissions on extreme weather events, either specific events or classes of events. A common approach to event attribution uses…

Methodology · Statistics 2018-02-06 Christopher J. Paciorek , Dáithí A. Stone , Michael F. Wehner

Random forest is a popular prediction approach for handling high dimensional covariates. However, it often becomes infeasible to interpret the obtained high dimensional and non-parametric model. Aiming for obtaining an interpretable…

Methodology · Statistics 2020-05-12 Jasper Velthoen , Juan-Juan Cai , Geurt Jongbloed

Over the last three decades, ensemble forecasts have become an integral part of forecasting the weather. They provide users with more complete information than single forecasts as they permit to estimate the probability of weather events by…

In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…

Statistics Theory · Mathematics 2021-12-21 Sébastien Farkas , Antoine Heranval , Olivier Lopez , Maud Thomas

This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…

Applications · Statistics 2015-09-04 Gianluca Rosso

We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of…

Applications · Statistics 2012-11-14 Massimiliano Ignaccolo , Marco Marani

Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper…

Machine Learning · Statistics 2025-07-25 Masaki Adachi , Masahiro Fujisawa , Michael A Osborne

This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…

Applications · Statistics 2025-04-03 Joan del Castillo , Pedro Puig

The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…

Atmospheric and Oceanic Physics · Physics 2026-01-06 Louise Largeau , Tom Beucler , David Leutwyler , Gregoire Mariethoz , Valerie Chavez-Demoulin , Erwan Koch

Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…

Methodology · Statistics 2024-04-16 Jordan Richards , Raphaël Huser

In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed…

Methodology · Statistics 2023-11-21 S. A. Padoan , Stefano Rizzelli

This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…

Applications · Statistics 2019-07-31 Amy L Wilson , Stan Zachary

We introduce the Tournament Rank Probability Score (TRPS) as a measure to evaluate and compare pre-tournament predictions, where predictions of the full tournament results are required to be available before the tournament begins. The TRPS…

Applications · Statistics 2019-12-17 Claus Thorn Ekstrøm , Hans Van Eetvelde , Christophe Ley , Ulf Brefeld