Statistical Methods in Particle Physics
"Statistics is the grammar of science." - Karl Pearson
For those of you who are keen to extend their education in the field of particle physics, it may be interesting to attend this course. The lecture and especially the hands-on exercises are particularly relevant for those who always wanted to know how to exactly interpret the discovery plot for the Higgs boson or the exclusion limits for New Physics at the LHC, and who are interested to learn more about data analysis techniques in general.
Supporting material
The following text books can be advised as a good starting point for graduate level students:
- Cowan: Statistical Data Analysis (Oxford Science Publications)
- Barlow: Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Manchester Physics Series)
- Lyons: Statistics for Nuclear and Particle Physicists (Cambridge University Press)
- P.R.Bevington and D.K.Robinson "Data reduction and error analysis for the physical sciences", WBC/McGrow-Hill, 1992
- Blobel, Lohrmann: Statistische Methoden der Datenanlyse (Teubner, in German) Ebook: http://www.desy.de/~blobel/eBuch.pdf
Formalia
Lectures (Link to LSF) every Monday 14:00 - 15:45 (note the changed time!), starting October 17th at INF 227 (KIP) / SR 3.404.
Tutorials every Monday 16:00 - 17:45, starting October 17th at CIP Pool, KIP / 1.401
Please sign up at Übungsgruppenverwaltung (electronic tutorial administration).
We will hand out an exercise sheet every week, the solutions for which have to be handed in electronically by email by Saturday 23h00 of the same week. The results will be discussed in the tutorial session on Monday of the following week (i.e. only one week later!), to ensure you get timely feedback.
The written exam will take place on 6 Feb 13:45-16:00 in nHS (SR) Philosophenweg 12. Please be on time, so that everybody is seated and we can start the actual exam at 14:00 sharp.
The results of the exams can be viewed (Klausureinsicht) on 13 Feb 11:00 - 13:00 at INF 227 (KIP) / SR 3.402 (next to the usual lecture room)
Contact:
Oleg Brandt oleg.brandt@kip.uni-heidelberg.de
Markus K. Köhler: mkoehler@physi.uni-heidelberg.de
Prerequisite knowledge
On the statistics side, there is no prerequisite knowledge, and we will (briefly) repeat the basic principles of statistics. On the particle physics side, the PEP4 lecture is sufficient, and the lecture can serve as a natural follow-up of PEP4 for Bachelor students interested in Particle Physics. Master students are invited to attend this lecture in parallel or after the Particle Physics course.
Lectures (dates to be fixed)
17.10.2016 | Lecture 1 | Overview + goals of the lecture course; Introduction to basic statistical tools |
24.10.2016 | Lecture 2 | Formal introduction to probability, Conditional probabilities, Bayes' theorem, Frequentist and Bayesian interpretation |
31.10.2016 | Lecture 3 | Probability density (PD) functions, fundamental PDs, useful-to-know PDs. |
7.11.2016 | Lecture 4 | Central limit theorem (CLT), statistical and systematic uncertainties, propagation of uncertainties, combination of uncorrelated measurements |
14.11.2016 | Lecture 5 | The Monte Carlo (MC) method, MC integration, MC simulation, generation of random numbers in [0,1] or distributed according to a PD |
21.11.2016 | Lecture 6 | Applications of MC simulation in HEP: event generation and detector simulation; Estimators and their properties |
28.11.2016 | Lecture 7 | Simple estimators for the mean and variance. The maximum likelihood (ML) method as an estimator |
5.12.2016 | Lecture 8 | Variance of ML estimators with the analytical, graphical, and MC methods, extended ML method, ML with binned data |
12.12.2016 | Lecture 9 | Connection between ML and Bayesian statistics, connection between ML and least squares methods. Hypothesis testing: goodness-of-fit test with Pearson's χ² and Kolmogorov-Smirnov |
19.12.2016 | Lecture 10 | Terminology of hypothesis testing, example using particle ID, Neyman-Pearson lemma, contructing a test statistic, significance of an observed signal using a Posson RV example |
2.1.2016 | NO lecture | |
9.1.2017 | Lecture 11 | Prediction intervals & limits; Bayesian credibility intervals, (frequentist) confidence intervals: Neyman construction, limits near a physical boundary |
16.1.2017 | Lecture 12 |
Feldman and Cousins limit construction, expected and observed limits, CL_{s} method, discovery. Homework reading: G. Aad (ATLAS Collaboration), "Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC", Phys. Lett. B, 716 1 (2012). |
23.1.2017 | Lecture 13 | Multivariate analysis (MVA) techniques: linear Fisher discriminant, neural networks, decision trees and boosted decison trees |
30.1.2017 | Lecture 14 | Unfolding techniques: bin-by-bin unfolding, regularised unfolding, iterative unfolding |
Additional reading
- Two nice papers where the CLs method is coherently explained (standard reference now): A.L. Read, "Modified frequentist analysis of search results (the CLs method)" CERN open-2000-205, follow-up "Presentation of search results: the CLs technique", J. Phys. G: Nucl. Part. Phys. 28 2693 (2002)).
- The application of MC techniques for event generation is very nicely described in a short article by Bryan Webber (pioneer of NLO MC generators).
Exercise sheets
- sheet 1
- sheet 2
- sheet 3
- sheet 4
- sheet 5
- sheet 6
- sheet 7
- sheet 8
- sheet 9
- sheet 10
- sheet 11
- sheet 12
- sheet 13
- sheet 14
Practice groups
- Group 1
20 participants
INF 227 / CIP-Pool KIP 1.401, Mon 16:00 - 18:00