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Most subjective probability aggregation procedures use a single probability judgment from each expert, even though it is common for experts studying real problems to update their probability estimates over time. This paper advances into…

Crowdsourcing enables the solicitation of forecasts on a variety of prediction tasks from distributed groups of people. How to aggregate the solicited forecasts, which may vary in quality, into an accurate final prediction remains a…

Methodology · Statistics 2022-03-31 Juntao Wang , Yang Liu , Yiling Chen

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

Conformal prediction provides a principled framework for uncertainty quantification with finite-sample coverage guarantees. While recent work has extended conformal prediction to online and sequential settings, existing methods typically…

Machine Learning · Statistics 2026-05-14 Eduardo Ochoa Rivera , Ambuj Tewari

A scoring rule is a function of a probabilistic forecast and a corresponding outcome that is used to evaluate forecast performance. A wide range of scoring rules have been defined over time and there is some debate as to which are the most…

Applications · Statistics 2019-08-27 Edward Wheatcroft

Probabilistic prediction systems often aggregate probability estimates from multiple models into a single decision. A common assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated.…

Machine Learning · Computer Science 2026-05-20 Zhaohui Wang

To mitigate the uncertainty of variable renewable resources, two off-the-shelf machine learning tools are deployed to forecast the solar power output of a solar photovoltaic system. The support vector machines generate the forecasts and the…

Machine Learning · Computer Science 2017-05-02 Mohamed Abuella , Badrul Chowdhury

Ensemble forecast post-processing is a necessary step in producing accurate probabilistic forecasts. Conventional post-processing methods operate by estimating the parameters of a parametric distribution, frequently on a per-location or…

Machine Learning · Computer Science 2023-05-01 Peter Mlakar , Janko Merše , Jana Faganeli Pucer

We present novel methods for predicting the outcome of large elections. Our first algorithm uses a diffusion process to model the time uncertainty inherent in polls taken with substantial calendar time left to the election. Our second model…

Applications · Statistics 2017-04-25 Dhruv Madeka

Ensemble weather forecasts enable a measure of uncertainty to be attached to each forecast, by computing the ensemble's spread. However, generating an ensemble with a good spread-error relationship is far from trivial, and a wide range of…

Atmospheric and Oceanic Physics · Physics 2021-01-05 Sebastian Scher , Gabriele Messori

Adaptive time series forecasting is essential for prediction under regime changes. Several classical methods assume linear Gaussian state space model (LGSSM) with variances constant in time. However, there are many real-world processes that…

Machine Learning · Statistics 2024-02-23 Baptiste Abélès , Joseph de Vilmarest , Olivier Wintemberger

To address the uncertainty in outputs of numerical weather prediction (NWP) models, ensembles of forecasts are used. To obtain such an ensemble of forecasts the NWP model is run multiple times, each time with different formulations and/or…

Applications · Statistics 2016-05-25 Annette Möller , Jürgen Groß

In recent years, probabilistic forecasting is an emerging topic, which is why there is a growing need of suitable methods for the evaluation of multivariate predictions. We analyze the sensitivity of the most common scoring rules,…

Methodology · Statistics 2019-10-17 Florian Ziel , Kevin Berk

In a supervised online setting, quantifying uncertainty has been proposed in the seminal work of \cite{gibbs2021adaptive}. For any given point-prediction algorithm, their method (ACI) produces a conformal prediction set with an average…

Statistics Theory · Mathematics 2025-11-24 Pierre Humbert , Ulysse Gazin , Ruth Heller , Etienne Roquain

Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields including meteorology, hydrology, economics, and demography. In typical applications, many alternative statistical…

Computation · Statistics 2018-07-31 Alexander Jordan , Fabian Krüger , Sebastian Lerch

In this paper we improve on the temperature predictions made with (online) Expert Aggregation (EA) [Cesa-Bianchi and Lugosi, 2006] in Part I. In particular, we make the aggregation more reactive, whilst maintaining at least the same root…

Optimization and Control · Mathematics 2025-06-19 Léo Pfitzner , Olivier Wintenberger , Olivier Mestre

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

An ensemble post-processing method is developed to improve the probabilistic forecasts of extreme precipitation events across the conterminous United States (CONUS). The method combines a 3-D Vision Transformer (ViT) for bias correction…

Atmospheric and Oceanic Physics · Physics 2025-09-17 Yingkai Sha , Ryan A. Sobash , David John Gagne

A well known problem with EOP prediction is that a prediction strategy proved to be the best for some testing period and prediction length may not remain as such for other period of time. In this paper we consider possible strategies to…

Geophysics · Physics 2009-11-20 Zinovy Malkin

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
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