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Distribution-free uncertainty estimation for ensemble methods is increasingly desirable due to the widening deployment of multi-modal black-box predictive models. Conformal prediction is one approach that avoids such distributional…

Methodology · Statistics 2025-05-26 Eduardo Ochoa Rivera , Yash Patel , Ambuj Tewari

Every prediction is ultimately used in a downstream task. Consequently, evaluating prediction quality is more meaningful when considered in the context of its downstream use. Metrics based solely on predictive performance often diverge from…

Machine Learning · Computer Science 2025-08-26 Novin Shahroudi , Viacheslav Komisarenko , Meelis Kull

We give an overview of some uses of proper scoring rules in statistical inference, including frequentist estimation theory and Bayesian model selection with improper priors.

Statistics Theory · Mathematics 2020-04-28 A. Philip Dawid , Monica Musio

We introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte-Carlo approximations of expectations and can therefore easily be evaluated for any…

The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which…

Theoretical Economics · Economics 2026-05-28 Dean P. Foster , Sergiu Hart

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

Forecasts support decision making in a variety of applications. Statistical models can produce accurate forecasts given abundant training data, but when data is sparse, rapidly changing, or unavailable, statistical models may not be able to…

Applications · Statistics 2020-05-19 Thomas McAndrew , Nutcha Wattanachit , G. Casey Gibson , Nicholas G. Reich

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

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Machine Learning · Computer Science 2024-04-22 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the the lowest expected score attributed to the true…

Methodology · Statistics 2021-02-01 Carol Alexander , Michael Coulon , Yang Han , Xiaochun Meng

Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…

Statistics Theory · Mathematics 2012-02-24 Tze Leung Lai , Shulamith T. Gross , David Bo Shen

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Machine Learning · Computer Science 2024-03-14 Sebastian G. Gruber , Florian Buettner

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

Given a set of items and a set of evaluators who all individually rank them, how do we aggregate these evaluations into a single societal ranking? Work in social choice and statistics has produced many aggregation methods for this problem,…

Computer Science and Game Theory · Computer Science 2025-08-26 Ratip Emin Berker , Ben Armstrong , Vincent Conitzer , Nihar B. Shah

Generalization to new samples is a fundamental rationale for statistical modeling. For this purpose, model validation is particularly important, but recent work in survey inference has suggested that simple aggregation of individual…

Methodology · Statistics 2024-04-15 Lauren Kennedy , Aki Vehtari , Andrew Gelman

All proper scoring rules incentivize an expert to predict \emph{accurately} (report their true estimate), but not all proper scoring rules equally incentivize \emph{precision}. Rather than treating the expert's belief as exogenously given,…

Computer Science and Game Theory · Computer Science 2021-06-01 Eric Neyman , Georgy Noarov , S. Matthew Weinberg

Scoring rules are an established way of comparing predictive performances across model classes. In the context of survival analysis, they require adaptation in order to accommodate censoring. This work investigates using scoring rules for…

Machine Learning · Computer Science 2024-11-14 Philipp Kopper , David Rügamer , Raphael Sonabend , Bernd Bischl , Andreas Bender

We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact…

Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…

Machine Learning · Statistics 2022-10-25 David Widmann , Fredrik Lindsten , Dave Zachariah

This paper forges a strong connection between two seemingly unrelated forecasting problems: incentive-compatible forecast elicitation and forecast aggregation. Proper scoring rules are the well-known solution to the former problem. To each…

Computer Science and Game Theory · Computer Science 2023-08-22 Eric Neyman , Tim Roughgarden