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Proper scoring rules are used to assess the out-of-sample accuracy of probabilistic forecasts, with different scoring rules rewarding distinct aspects of forecast performance. Herein, we re-investigate the practice of using proper scoring…

When predicting future events, it is common to issue forecasts that are probabilistic, in the form of probability distributions over the range of possible outcomes. Such forecasts can be evaluated using proper scoring rules. Proper scoring…

Computation · Statistics 2023-05-15 Sam Allen

In situations where forecasters are scored on the quality of their probabilistic predictions, it is standard to use `proper' scoring rules to perform such scoring. These rules are desirable because they give forecasters no incentive to lie…

Methodology · Statistics 2020-08-25 Spencer Greenberg

We introduce several new estimation methods that leverage shape constraints in auction models to estimate various objects of interest, including the distribution of a bidder's valuations, the bidder's ex ante expected surplus, and the…

Econometrics · Economics 2019-12-17 Joris Pinkse , Karl Schurter

Survey sampling is concerned with the estimation of finite population parameters. In practice, survey data suffer from item nonresponse, which is commonly handled through imputation, i.e., replacing missing values with predicted values. As…

Methodology · Statistics 2026-03-06 Ziming An , Mehdi Dagdoug , David Haziza

Weighting estimators based on propensity scores are widely used for causal estimation in a variety of contexts, such as observational studies, marginal structural models and interference. They enjoy appealing theoretical properties such as…

Methodology · Statistics 2021-10-06 Linbo Wang , Yuexia Zhang , Thomas S. Richardson , Xiao-Hua Zhou

I introduce a model of predictive scoring. A receiver wants to predict a sender's quality. An intermediary observes multiple features of the sender and aggregates them into a score. Based on the score, the receiver makes a decision. The…

Theoretical Economics · Economics 2024-05-17 Ian Ball

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

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

Scoring rules for eliciting expert predictions of random variables are usually developed assuming that experts derive utility only from the quality of their predictions (e.g., score awarded by the rule, or payoff in a prediction market). We…

Computer Science and Game Theory · Computer Science 2011-06-14 Craig Boutilier

Given a learning problem with real-world tradeoffs, which cost function should the model be trained to optimize? This is the metric selection problem in machine learning. Despite its practical interest, there is limited formal guidance on…

Machine Learning · Statistics 2022-08-22 Gaurush Hiranandani

We discuss a new weighted likelihood method for parametric estimation. The method is motivated by the need for generating a simple estimation strategy which provides a robust solution that is simultaneously fully efficient when the model is…

Methodology · Statistics 2019-08-29 Suman Majumder , Adhidev Biswas , Tania Roy , Subir Kumar Bhandari , Ayanendranath Basu

What is a fair performance metric? We consider the choice of fairness metrics through the lens of metric elicitation -- a principled framework for selecting performance metrics that best reflect implicit preferences. The use of metric…

Machine Learning · Statistics 2020-11-04 Gaurush Hiranandani , Harikrishna Narasimhan , Oluwasanmi Koyejo

Strictly proper scoring rules (SPSR) are incentive compatible for eliciting information about random variables from strategic agents when the principal can reward agents after the realization of the random variables. They also quantify the…

Computer Science and Game Theory · Computer Science 2020-06-09 Yang Liu , Juntao Wang , Yiling Chen

Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…

Statistics Theory · Mathematics 2020-04-28 Philip Dawid , Monica Musio , Laura Ventura

Assessing the fairness of a decision making system with respect to a protected class, such as gender or race, is challenging when class membership labels are unavailable. Probabilistic models for predicting the protected class based on…

Applications · Statistics 2018-11-28 Jiahao Chen , Nathan Kallus , Xiaojie Mao , Geoffry Svacha , Madeleine Udell

We study fairness in decision-making when the data may encode systematic bias. Existing approaches typically impose fairness constraints while predicting the observed decision, which may itself be unfair. We propose a novel framework for…

Methodology · Statistics 2026-03-31 Ping Zhang , Naiwen Ying , Wang Miao

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

Given a binary prediction problem, which performance metric should the classifier optimize? We address this question by formalizing the problem of Metric Elicitation. The goal of metric elicitation is to discover the performance metric of a…

Machine Learning · Statistics 2019-01-21 Gaurush Hiranandani , Shant Boodaghians , Ruta Mehta , Oluwasanmi Koyejo

Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probability distributions. In this article, we review the…

Statistics Theory · Mathematics 2026-05-12 Kartik Waghmare , Johanna Ziegel
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