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The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems,…

Discrete Mathematics · Computer Science 2020-11-05 Héctor Cancela , Gustavo Guerberoff , Franco Robledo , Pablo Romero

In power system operation, characterizing the stochastic nature of wind power is an important albeit challenging issue. It is well known that distributions of wind power forecast errors often exhibit significant variability with respect to…

Data Analysis, Statistics and Probability · Physics 2017-12-05 Zhiwen Wang , Chen Shen , Feng Liu

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

A user-focused verification approach for evaluating probability forecasts of binary outcomes (also known as probabilistic classifiers) is demonstrated that is (i) based on proper scoring rules, (ii) focuses on user decision thresholds, and…

Applications · Statistics 2024-03-25 Nicholas Loveday , Robert Taggart , Mohammadreza Khanarmuei

Probabilistic temperature forecasts are potentially useful to the energy and weather derivatives industries. However, at present, they are little used. There are a number of reasons for this, but we believe this is in part due to…

Atmospheric and Oceanic Physics · Physics 2007-05-23 Stephen Jewson , Christine Ziehmann

The climate response to anthropogenic forcing has long been one of the dominant uncertainties in predicting future climate change (Houghton et al, 2001). Many observationally-based estimates of climate sensitivity (S) have been presented in…

Atmospheric and Oceanic Physics · Physics 2007-05-23 J. D. Annan , J. C. Hargreaves

We initiate the study of the truthfulness of calibration measures in sequential prediction. A calibration measure is said to be truthful if the forecaster (approximately) minimizes the expected penalty by predicting the conditional…

Machine Learning · Computer Science 2024-11-22 Nika Haghtalab , Mingda Qiao , Kunhe Yang , Eric Zhao

Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…

Artificial Intelligence · Computer Science 2022-10-18 Ang Li , Judea Pearl

Scoring rules are an important tool for evaluating the performance of probabilistic forecasting schemes. In the binary case, scoring rules (which are strictly proper) allow for a decomposition into terms related to the resolution and to the…

Atmospheric and Oceanic Physics · Physics 2015-05-13 Jochen Bröcker

We show that probabilistic weather forecasts of site specific temperatures can be dramatically improved by using seasonally varying rather than constant calibration parameters.

Atmospheric and Oceanic Physics · Physics 2007-05-23 Stephen Jewson

For applications of machine learning in critical decisions, explainability is a primary concern, and often a regulatory requirement. Local linear methods for generating explanations, such as LIME and SHAP, have been criticized for being…

Machine Learning · Computer Science 2026-03-25 Joseph L. Breeden

We present a scheme by which a probabilistic forecasting system whose predictions have poor probabilistic calibration may be recalibrated by incorporating past performance information to produce a new forecasting system that is demonstrably…

Methodology · Statistics 2019-04-08 Carlo Graziani , Robert Rosner , Jennifer M. Adams , Reason L. Machete

Systematically biased forecasts are typically interpreted as evidence of forecasters' irrationality and/or asymmetric loss. In this paper we propose an alternative explanation: when forecasts inform policy decisions, and the resulting…

Theoretical Economics · Economics 2026-04-24 Robert P. Lieli , Augusto Nieto-Barthaburu

Selective prediction [Dru13, QV19] models the scenario where a forecaster freely decides on the prediction window that their forecast spans. Many data statistics can be predicted to a non-trivial error rate without any distributional…

Machine Learning · Computer Science 2025-08-14 Licheng Liu , Mingda Qiao

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

Machine Learning · Computer Science 2024-08-08 Agathe Fernandes Machado , Arthur Charpentier , Emmanuel Flachaire , Ewen Gallic , François Hu

Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…

Methodology · Statistics 2016-03-02 Sarah Higgins , Hailiang Du , Leonard A. Smith

In order to identify expertise, forecasters should not be tested by their calibration score, which can always be made arbitrarily small, but rather by their Brier score. The Brier score is the sum of the calibration score and the refinement…

Theoretical Economics · Economics 2026-03-20 Dean P. Foster , Sergiu Hart

In public discussions of the quality of forecasts, attention typically focuses on the predictive performance in cases of extreme events. However, the restriction of conventional forecast evaluation methods to subsets of extreme observations…

The output of solar power generation is significantly dependent on the available solar radiation. Thus, with the proliferation of PV generation in the modern power grid, forecasting of solar irradiance is vital for proper operation of the…

Applications · Statistics 2022-09-05 Kwasi Opoku , Svetlana Lucemo , Qun Zhou Sun , Aleksandar Dimitrovski

The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their…

Machine Learning · Computer Science 2025-07-18 Anurag Singh , Siu Lun Chau , Krikamol Muandet