Physics:Quantum data analysis/Moments
Moments summarize the shape of a distribution through quantities such as mean, variance, skewness, kurtosis, or higher weighted averages. In particle-physics analysis, moments can describe multiplicity fluctuations, angular distributions, energy flow, event shapes, and response functions. They condense complex distributions into numbers that can be compared across datasets, models, or event classes. The first moments describe location and spread, while higher moments probe asymmetry and tails. In finite data samples, moment estimates have statistical uncertainty and can be sensitive to outliers or acceptance edges. Moments are used in fluctuation studies, angular analyses, structure-function measurements, and comparisons of reconstructed and generated distributions.
Statistical meaning
The first moments describe location and spread, while higher moments probe asymmetry and tails. In finite data samples, moment estimates have statistical uncertainty and can be sensitive to outliers or acceptance edges.[1]
Physics use
Moments are used in fluctuation studies, angular analyses, structure-function measurements, and comparisons of reconstructed and generated distributions. Weighted moments can emphasize particular kinematic regions.[2]
Cautions
A few moments do not uniquely determine a distribution. For interpretation they should be accompanied by bin-by-bin checks, systematic variations, and clear definitions of the event sample and phase space.[3]
Overview
Moments is used in particle-physics data analysis to turn detector output, simulated samples, and theoretical models into quantitative physics results. In high-energy experiments the term is connected with event selection, calibration, uncertainty treatment, validation, and comparison with Standard Model or beyond-Standard-Model predictions.
Analysis role
The analysis task is usually defined by the observable being measured or the signal being searched for. A robust workflow keeps raw detector information, reconstructed objects, simulated events, control samples, and statistical models traceable so that assumptions can be checked and systematic uncertainties can be propagated.
Practical considerations
In practice, moments must be documented with selection definitions, units, binning choices, correction factors, and reproducible code or configuration. This makes the result easier to compare across experiments and easier to reinterpret when improved simulations, calibrations, or theoretical predictions become available.[4]
See also
Table of contents (60 articles)
Index
Full contents
References
- ↑ Cowan, Glen (1998). Statistical Data Analysis. Oxford University Press. ISBN 978-0-19-850156-5.
- ↑ "Review of Particle Physics". Physical Review D 110 (3): 030001. 2024. doi:10.1103/PhysRevD.110.030001.
- ↑ Lyons, Louis (1986). Statistics for Nuclear and Particle Physicists. Cambridge University Press. ISBN 978-0-521-37934-2.
- ↑ "Review of Particle Physics". Physical Review D 110 (3): 030001. 2024. doi:10.1103/PhysRevD.110.030001.
Source attribution: Physics:Quantum data analysis/Moments
