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The Brier score is frequently used by meteorologists to measure the skill of binary probabilistic forecasts. We show, however, that in simple idealised cases it gives counterintuitive results. We advocate the use of an alternative measure…

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

The Brier Score is a widely-used criterion to assess the quality of probabilistic predictions of binary events. The expectation value of the Brier Score can be decomposed into the sum of three components called reliability, resolution, and…

Methodology · Statistics 2014-01-03 Stefan Siegert

As advancements in novel biomarker-based algorithms and models accelerate disease risk prediction and stratification in medicine, it is crucial to evaluate these models within the context of their intended clinical application. Prediction…

Methodology · Statistics 2025-09-11 Kehao Zhu , Yingye Zheng , Kwun Chuen Gary Chan

Three paediatric cardiologists assessed nearly 1000 imprecise subjective conditional probabilities for a simple belief network representing congenital heart disease, and the quality of the assessments has been measured using prospective…

Artificial Intelligence · Computer Science 2013-04-08 David J. Spiegelhalter , Rodney C. Franklin , Kate Bull

The Brier score is commonly used for evaluating probability predictions. In survival analysis, with right-censored observations of the event times, this score can be weighted by the inverse probability of censoring (IPCW) to retain its…

Machine Learning · Statistics 2019-12-19 Håvard Kvamme , Ørnulf Borgan

Machine learning-supported decisions, such as ordering diagnostic tests or determining preventive custody, often require converting probabilistic forecasts into binary classifications. We adopt a consequentialist perspective from decision…

Machine Learning · Computer Science 2026-03-11 Gerardo Flores , Abigail Schiff , Alyssa H. Smith , Julia A Fukuyama , Ashia C. Wilson

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound).…

Machine Learning · Computer Science 2023-11-21 Gundeep Arora , Srujana Merugu , Anoop Saladi , Rajeev Rastogi

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

This article explores the extension of well-known F1 score used for assessing the performance of binary classifiers. We propose the new metric using probabilistic interpretation of precision, recall, specificity, and negative predictive…

Machine Learning · Computer Science 2024-04-17 Mikolaj Sitarz

Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about…

Methodology · Statistics 2023-08-14 X. M. Kavelaars , J. Mulder , M. C. Kaptein

Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and…

Machine Learning · Computer Science 2023-10-20 Attila Fazekas , György Kovács

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

Variance in predictions across different trained models is a significant, under-explored source of error in fair binary classification. In practice, the variance on some data examples is so large that decisions can be effectively arbitrary.…

In the face of uncertainty, the need for probabilistic assessments has long been recognized in the literature on forecasting. In classification, however, comparative evaluation of classifiers often focuses on predictions specifying a single…

Methodology · Statistics 2023-05-31 Johannes Resin

Prediction algorithms that quantify the expected benefit of a given treatment conditional on patient characteristics can critically inform medical decisions. Quantifying the performance of treatment benefit prediction algorithms is an…

Methodology · Statistics 2023-05-17 Yuan Xia , Paul Gustafson , Mohsen Sadatsafavi

The adequate use of information measured in a continuous manner along a period of time represents a methodological challenge. In the last decades, most of traditional statistical procedures have been extended for accommodating these…

Methodology · Statistics 2025-12-04 Pablo Martinez-Camblor

This document provides a brief overview of different metrics and terminology that is used to measure the performance of binary classification systems.

Machine Learning · Computer Science 2014-10-21 Sebastian Raschka

Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…

Methodology · Statistics 2026-03-18 Oliver L. Pescott , Robin J. Boyd , Gary D. Powney , Gavin B. Stewart

In a binary classification problem the feature vector (predictor) is the input to a scoring function that produces a decision value (score), which is compared to a particular chosen threshold to provide a final class prediction (output).…

Machine Learning · Computer Science 2021-11-11 Waleed A. Yousef

Inter-rater reliability (IRR) is one of the commonly used tools for assessing the quality of ratings from multiple raters. However, applicant selection procedures based on ratings from multiple raters usually result in a binary outcome; the…

Methodology · Statistics 2025-06-17 František Bartoš , Patrícia Martinková
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