Statistical Methods in Particle Physics

winter term 2016/2017
Lecturer: Priv.-Doz. Dr. Oleg Brandt
Link to LSF
20 participants


"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:


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)


Oleg Brandt

Markus K. Köhler:

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, CLs 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

Exercise sheets

Practice groups

Statistical Methods in Particle Physics
winter term 2016/2017
Link zum LSF
20 participants