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Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted…

Data Analysis, Statistics and Probability · Physics 2014-11-18 Rajendran Raja

As Large Language Models (LLMs) are increasingly integrated in diverse applications, obtaining reliable measures of their predictive uncertainty has become critically important. A precise distinction between aleatoric uncertainty, arising…

Evaluation of per-sample uncertainty quantification from neural networks is essential for decision-making involving high-risk applications. A common approach is to use the predictive distribution from Bayesian or approximation models and…

Machine Learning · Computer Science 2025-09-12 H. Martin Gillis , Isaac Xu , Thomas Trappenberg

Uncertainty decomposition refers to the task of decomposing the total uncertainty of a predictive model into aleatoric (data) uncertainty, resulting from inherent randomness in the data-generating process, and epistemic (model) uncertainty,…

Computation and Language · Computer Science 2024-06-12 Bairu Hou , Yujian Liu , Kaizhi Qian , Jacob Andreas , Shiyu Chang , Yang Zhang

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…

Applications · Statistics 2017-06-09 Mikael Kuusela , Philip B. Stark

Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…

Artificial Intelligence · Computer Science 2013-02-18 Henry E. Kyburg

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

Computer Vision and Pattern Recognition · Computer Science 2026-02-19 M. M. A. Valiuddin , R. J. G. van Sloun , C. G. A. Viviers , P. H. N. de With , F. van der Sommen

When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input distributions estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance…

Methodology · Statistics 2020-11-10 Wei Xie , Barry L. Nelson , Russell R. Barton

Universal shape profiles in a variety of systems contain crucial information on the underlying dynamics. We develop such shape profiles for earthquakes as a stronger test of theory against observations. The earthquake analysis shows good…

Statistical Mechanics · Physics 2007-05-23 Amit P. Mehta , Karin A. Dahmen , Yehuda Ben-Zion

A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the…

Data Analysis, Statistics and Probability · Physics 2015-05-20 P. D. Dauncey , M. Kenzie , N. Wardle , G. J. Davies

I consider the uncertainties in parton distributions and the consequences for hadronic cross-sections. There is ever-increasing sophistication in the relationship between the uncertainties of the distributions and the errors on the…

High Energy Physics - Phenomenology · Physics 2007-11-20 R. S. Thorne

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work…

Machine Learning · Computer Science 2023-04-24 Sebastian G. Gruber , Florian Buettner

The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…

Numerical Analysis · Mathematics 2020-03-12 Sergey P. Shary

Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…

Machine Learning · Computer Science 2024-10-15 Yuko Kato , David M. J. Tax , Marco Loog

When undertaking cyber security risk assessments, we must assign numeric values to metrics to compute the final expected loss that represents the risk that an organization is exposed to due to cyber threats. Even if risk assessment is…

Computer Science and Game Theory · Computer Science 2017-12-19 Andrew Fielder , Sandra Konig , Emmanouil Panaousis , Stefan Schauer , Stefan Rass

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

Artificial Intelligence · Computer Science 2013-03-26 Arthur Ramer

Understanding why a large language model (LLM) is uncertain about the response is important for their reliable deployment. Current approaches, which either provide a single uncertainty score or rely on the classical aleatoric-epistemic…

Artificial Intelligence · Computer Science 2026-03-27 Aditya Taparia , Ransalu Senanayake , Kowshik Thopalli , Vivek Narayanaswamy

Spatial dynamic microsimulations probabilistically project geographically referenced units with individual characteristics over time. Like any projection method, their outcomes are inherently uncertain and sensitive to multiple factors.…

Computation · Statistics 2025-11-19 Morgane Dumont , Ahmed Alsaloum , Julian Ernst , Jan Weymeirsch , Ralf Münnich

General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

Quantum Physics · Physics 2012-12-18 Yoshimasa Kurihara

Quantifying and managing uncertainties that occur when data-driven models such as those provided by AI and machine learning methods are applied is crucial. This whitepaper provides a brief motivation and first overview of the state of the…

Machine Learning · Computer Science 2018-11-29 Michael Kläs