Physics:Quantum data analysis/Integral Correlation functions: Difference between revisions
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'''Integral correlation functions''' reduce correlation information to quantities integrated over a selected region of phase space. They are useful when the goal is to compare total correlation strength, fluctuation magnitude, or cumulative structure across event classes. The price of integration is loss of detailed shape information, so the integration region must be physically motivated and clearly documented.<ref name="cowan">{{cite book |last=Cowan |first=Glen |title=Statistical Data Analysis |publisher=Oxford University Press |year=1998 |isbn=978-0-19-850156-5}}</ref> | |||
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[[File:Quantum_data_analysis_integral_correlation_functions_yellow.png|thumb|280px|Integral | [[File:Quantum_data_analysis_integral_correlation_functions_yellow.png|thumb|280px|Integral correlation functions represented as summarized event-level correlation strength.]] | ||
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== Definition == | |||
An integral correlation is obtained by summing or integrating a differential correlation over specified bins, ranges, or weights. The result depends on the chosen acceptance, normalization, and reference sample.<ref name="cowan">{{cite book |last=Cowan |first=Glen |title=Statistical Data Analysis |publisher=Oxford University Press |year=1998 |isbn=978-0-19-850156-5}}</ref> | |||
== Use cases == | |||
Integrated quantities are useful for comparing models, measuring global fluctuations, summarizing collective effects, and reporting compact observables. They are often more stable statistically than finely binned differential correlations.<ref name="lyons">{{cite book |last=Lyons |first=Louis |title=Statistics for Nuclear and Particle Physicists |publisher=Cambridge University Press |year=1986 |isbn=978-0-521-37934-2}}</ref> | |||
== Limitations == | |||
Because different physical mechanisms can contribute to the same integrated value, integral correlations should be interpreted together with differential checks, control regions, and systematic variations.<ref name="pdg2024">{{cite journal |collaboration=Particle Data Group |title=Review of Particle Physics |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |year=2024 |doi=10.1103/PhysRevD.110.030001}}</ref> | |||
=See also= | =See also= | ||
Revision as of 20:57, 19 May 2026
Integral correlation functions reduce correlation information to quantities integrated over a selected region of phase space. They are useful when the goal is to compare total correlation strength, fluctuation magnitude, or cumulative structure across event classes. The price of integration is loss of detailed shape information, so the integration region must be physically motivated and clearly documented.[1]
Definition
An integral correlation is obtained by summing or integrating a differential correlation over specified bins, ranges, or weights. The result depends on the chosen acceptance, normalization, and reference sample.[1]
Use cases
Integrated quantities are useful for comparing models, measuring global fluctuations, summarizing collective effects, and reporting compact observables. They are often more stable statistically than finely binned differential correlations.[2]
Limitations
Because different physical mechanisms can contribute to the same integrated value, integral correlations should be interpreted together with differential checks, control regions, and systematic variations.[3]
See also
Table of contents (60 articles)
Index
Foundations and experiments
Analysis, measurements and discovery
Full contents
1. Introduction to Particle Physics (5) Back to index
2. Nuts and Bolts (4) Back to index
3. Overview of Particle Collision Experiments (3) Back to index
4. Collision Kinematics and Complex Observables (8) Back to index
5. Basic Measurements (4) Back to index
6. Data Acquisition Electronics and Systems (1) Back to index
7. Event Reconstruction (3) Back to index
8. Monte Carlo Simulations (4) Back to index
9. General Statistical Methods and Data Visualisation (6) Back to index
10. Standard Model Measurements (6) Back to index
11. Searches for New Physics (4) Back to index
12. Data Processing Techniques (4) Back to index
13. Fit Optimisation Techniques (4) Back to index
14. Advanced Data Comprehension Techniques (3) Back to index
15. Machine Learning (1) Back to index
60. Machine Learning
References
- ↑ 1.0 1.1 Cowan, Glen (1998). Statistical Data Analysis. Oxford University Press. ISBN 978-0-19-850156-5.
- ↑ 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.
Author: Sergei V. Chekanov
Author: Claude Pruneau
Author: Harold Foppele
Source attribution: Physics:Quantum data analysis/Integral Correlation functions
