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We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection…

Methodology · Statistics 2016-12-20 Yoshiyuki Ninomiya , Satoshi Kuriki , Toshihiko Shiroishi , Toyoyuki Takada

Probabilistic forecasts are typically obtained using state-of-the-art statistical and machine learning models, with model parameters estimated by optimizing a proper scoring rule over a set of training data. If the model class is not…

Applications · Statistics 2026-05-05 Jakob Benjamin Wessel , Maybritt Schillinger , Frank Kwasniok , Sam Allen

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting…

Methodology · Statistics 2021-08-26 Timo Dimitriadis , Tilmann Gneiting , Alexander I. Jordan

A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…

Machine Learning · Statistics 2014-01-14 Mahdi Pakdaman Naeini , Gregory F. Cooper , Milos Hauskrecht

We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of…

Machine Learning · Statistics 2019-05-16 Hao Song , Tom Diethe , Meelis Kull , Peter Flach

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…

The gold standard for identifying causal relationships is a randomized controlled experiment. In many applications in the social sciences and medicine, the researcher does not control the assignment mechanism and instead may rely upon…

Applications · Statistics 2016-11-22 Johann Gagnon-Bartsch , Yotam Shem-Tov

Conditional independence testing (CIT) is a common task in machine learning, e.g., for variable selection, and a main component of constraint-based causal discovery. While most current CIT approaches assume that all variables are numerical…

Machine Learning · Computer Science 2023-11-07 Oana-Iuliana Popescu , Andreas Gerhardus , Jakob Runge

Conformalized multiple testing offers a model-free way to control predictive uncertainty in decision-making. Existing methods typically use only part of the available data to build score functions tailored to specific settings. We propose a…

Methodology · Statistics 2026-05-22 Yuyang Huo , Xiaoyang Wu , Changliang Zou , Haojie Ren

Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures…

Machine Learning · Computer Science 2020-08-11 Jeremy Nixon , Mike Dusenberry , Ghassen Jerfel , Timothy Nguyen , Jeremiah Liu , Linchuan Zhang , Dustin Tran

Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights.…

Methodology · Statistics 2023-05-30 Chenyin Gao , Shu Yang , Jae Kwang Kim

The use of tiered warnings and multicategorical forecasts are ubiquitous in meteorological operations. Here, a flexible family of scoring functions is presented for evaluating the performance of ordered multicategorical forecasts. Each…

Applications · Statistics 2022-05-02 Robert Taggart , Nicholas Loveday , Deryn Griffiths

This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to…

Machine Learning · Statistics 2023-06-27 Takuo Matsubara , Niek Tax , Richard Mudd , Ido Guy

Machine learning approaches for image classification have led to impressive advances in that field. For example, convolutional neural networks are able to achieve remarkable image classification accuracy across a wide range of applications…

Machine Learning · Statistics 2025-10-30 Christopher T. Franck , Anne R. Driscoll , Zoe Szajnfarber , William H. Woodall

Post-hoc calibration methods are widely used to improve the reliability of probabilistic predictions from machine learning models. Despite their prevalence, a comprehensive theoretical understanding of these methods remains elusive,…

Machine Learning · Computer Science 2025-09-30 Kristina P. Sinaga , Arjun S. Nair

While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to the same degree. Uncertainty methods are designed to provide…

Machine Learning · Statistics 2020-06-17 Adam M. Oberman , Chris Finlay , Alexander Iannantuono , Tiago Salvador

Survival analysis deals with modeling the time until an event occurs, and accurate probability estimates are crucial for decision-making, particularly in the competing-risks setting where multiple events are possible. While recent work has…

Methodology · Statistics 2026-02-03 Julie Alberge , Tristan Haugomat , Gaël Varoquaux , Judith Abécassis

The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…

Machine Learning · Statistics 2023-06-06 Wenlu Tang , Zicheng Liu

Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable. It is popular as it comes with theoretical guarantees on…

Machine Learning · Statistics 2025-12-01 Jase Clarkson , Wenkai Xu , Mihai Cucuringu , Yvik Swan , Gesine Reinert

Monte Carlo techniques are the method of choice for making probabilistic predictions of an outcome in several disciplines. Usually, the aim is to generate calibrated predictions which are statistically indistinguishable from the outcome.…

Methodology · Statistics 2025-07-01 Sándor Baran , Martin Leutbecher
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