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Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…

Machine Learning · Computer Science 2025-12-16 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…

Data Analysis, Statistics and Probability · Physics 2015-10-28 Jens Erler

The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties,…

Nuclear Theory · Physics 2018-12-10 Sota Yoshida , Noritaka Shimizu , Tomoaki Togashi , Takaharu Otsuka

The measurements with the background estimation from an off-zone are widely used in astrophysics, accelerator physics and other areas. Usually, the expected number of the background events in the off-zone and in the on-zone is known with a…

Applications · Statistics 2013-05-02 Vladimir Kulikovskiy

We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…

Methodology · Statistics 2025-09-04 P. Algikar , P. Sharma , M. Netto , L. Mili

Subjective judgements from experts provide essential information when assessing and modelling threats in respect to cyber-physical systems. For example, the vulnerability of individual system components can be described using multiple…

Cryptography and Security · Computer Science 2019-10-03 Zack Ellerby , Josie McCulloch , Melanie Wilson , Christian Wagner

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Probability · Mathematics 2020-06-16 Xinjia Chen

The proper choice of a measurement technique that minimizes systematic and random uncertainty is an essential part of experimental physics. These issues are difficult to teach in the introductory laboratory, though: because most experiments…

Physics Education · Physics 2011-08-26 Chad Orzel , Gary Reich , Jonathan Marr

To properly estimate signal significance while accounting for both statistical and systematic uncertainties, we conducted a study to analyze the impact of typical systematic uncertainties, such as background shape, signal shape, and the…

Data Analysis, Statistics and Probability · Physics 2023-12-19 Yi Ding , Weiming Song , Kai Zhu

In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…

Statistics Theory · Mathematics 2020-12-21 Sebastian Kersting , Michael Kohler

Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We…

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…

Quantum Physics · Physics 2016-04-19 V. I. Yukalov , D. Sornette

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…

Machine Learning · Statistics 2025-02-18 Nikita Kotelevskii , Vladimir Kondratyev , Martin Takáč , Éric Moulines , Maxim Panov

The incorporation of uncertainties to calculations of signal significance in planned experiments is an actual task. Several approaches to this problem are discussed. We present a procedure for taking into account the systematic uncertainty…

High Energy Physics - Phenomenology · Physics 2009-11-07 S. I. Bityukov

How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…

Applications · Statistics 2022-11-15 Akisato Suzuki

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…

Computation and Language · Computer Science 2024-10-22 Hsiu-Yuan Huang , Yutong Yang , Zhaoxi Zhang , Sanwoo Lee , Yunfang Wu

Roughness parameters that characterize contacting surfaces with regard to friction and wear are commonly stated without uncertainties, or with an uncertainty only taking into account a very limited amount of aspects such as repeatability of…

Data Analysis, Statistics and Probability · Physics 2016-07-20 Dorothee Hüser , Jonathan Hüser , Sebastian Rief , Jörg Seewig , Peter Thomsen-Schmidt

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…

Quantitative Methods · Quantitative Biology 2025-08-27 Michael J. Plank , Matthew J. Simpson

Economic assessment in environmental science concerns the measurement or valuation of environmental impacts, adaptation, and vulnerability. Integrated assessment modeling is a unifying framework of environmental economics, which attempts to…

General Economics · Economics 2020-09-02 Ruda Zhang , Patrick Wingo , Rodrigo Duran , Kelly Rose , Jennifer Bauer , Roger Ghanem

Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned…

High Energy Physics - Experiment · Physics 2011-07-13 Mike Williams