Statistical Methods in Particle Physics

winter term 2021/2022
Lecturer: Stamen Reygers
Link to LSF
26 participants

Niels Bohr supposedly said if quantum mechanics did not make you dizzy then you did not really understand it. I think the same can be said about statistical inference. 

Robert D. Cousins, Why isn't every physicist a Bayesian

Learning goals and required knowledge

This course is a natural follow-up to PEP4 for Bachelor students interested in Particle Physics. Master students are invited to attend this lecture in parallel or after the Particle Physics course

Learning goals

  • Get to know and apply the toolbox of statistical methods used in particle physics
  • Understand error bars and confidence limts as reported in publications
  • Solid understanding of maximum likelihood and least squares fits
  • From measurement to message: which conclusion can you draw from your data (and which not)?
  • Learn to apply machine learning methods

Required knowledge

  • Basic understanding of experimental particle physics (as taught in the bachelor's course)
  • Basic knowledge of python is needed (see below)


Links to slides appear in red:

  1. Basics concepts
    • Probability
    • Mean, median, mode
    • Covariance and correlation
  2. Probability distributions
  3. Uncertainty
    • Statistical and systematic uncertainties
    • Propagation of uncertainties
    • Combination of uncorrelated measurements
  4. Monte Carlo and numerical methods
    • Generation of random numbers
    • Monte Carlo integration
    • Applications in HEP
  5. Maximum likelihood estimation
    • Basics: consistency, bias, efficiency
    • Maximum likelihood method
  6. Method of least squares
  7. Goodness-of-fit and hypthesis testing
  8. Confidence limits and intervals
    • Neyman construction
    • Feldman-Cousins confidence intervals
  9. Machine Learning
    • General Overview: machine learning, deep learning and all that
    • Neural Networks
    • Boosted Decision trees
  10. Unfolding
    • Response matrix
    • Regularized unfolding
    • "Bayesian" unfolding

A. Selected topics

  1. Kalman filter (Martin Völkl)
  2. MNIST classification with a simple convolutional neural network using Keras
  3. Practical tips
  4. Advanced topics in Bayesian Statistics (Martin Völkl)
  5. Symbolic regression

Lecture videos

Week 1 (21 Oct 2020)

Week 2 (28 Oct 2021)

Week 3 (4 Nov 2021)

Week 4 (11 Nov 2021)

Week 5 (18 Nov 2021)

Week 6 (25 Nov 2021)

Week 7 (2 Dec 2021)

Week 8 (9 Dec 2021)

Week 9 (16 Dec 2021)

Week 10 (13 January 2022)

Week 11 (20 January 2022)

Week 12 (27 January 2022)

Practical Information


  • Format: flipped/inverted classroom
  • Thursday meetings start at 17:00 (via zoom)
  • The zoom link for the meeting will be send to the registered people by email prior to the first lecture on October 21st.
  • Lectures will be provided as videos (screencasts) and can be accessed any time. Videos are made available every week on Tuesday evening. This allows you a to study the material in a flexible way even in case of overlap with other lectures/seminars.
  • Slides will be made available as well.
  • Contact time during the video meetings on Thursdays will only be used to discuss questions and do quizzes. This should take about 30 min.
  • Question sent before the Thurday meeting (email,, ...) are very welcome


  • Tutorials will be in presence in the KIP CIP pool 
  • Group 1 (Mo: 16:00 - 17:45)
  • Group 2 (Tu 16:00 - 17:45) 
  • First tutorial: October 25/26, 2021
  • Used software: python + jupyter notebooks
  • The KIP Jupyter server can be used to work on the exercises from any browser
  • You can also install Jupyter notesbooks on you own computer


  • You need to register for this course

Exercise sheets

  • will be handed out every week after the lecture 
  • can be downloaded from this web page
  • to be handed in by Thursday, 10:00 of the following week
  • should be handed in electronically using the Übungsgruppenverwaltung
  • will be handed out as jupyter notebooks
  • should be handed in as jupityer notebooks or as pdf file. (e.g. scan of a handwritten solution)
  • At least 60% of the points are needed to qualify for the exam.


  • Date: to be defined
  • Format: most likely in presence
  • The grade for this course is the grade of the exam

ECTS points

  • Lecture and tutorials: 4 ECTS points


  • A large fraction (>50%) of the problems consist of the implementation of statistical methods in Python in the framework of jupyter notebooks.
  • A basic level of knowledge in Python is needed. Advanced modules will be used but special knowledge is not needed prior to the lecture.
  • There are several good tutorials and courses on the internet which you can use to acquire a basic programming level.
  • The tutorials start only in the second week and the first problem sheet will be handed out on Thursday of the first week. So you might consider the first few days to go through some of these Python courses.


  • G. Cowan, Statistical Data Analysis
  • Behnke, Kroeninger, Schott, Schoerner-Sadenius: Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods
  • Claude A. Pruneau, Data Analysis Techniques for Physical Scientists
  • L. Lista, Statistical Methods for Data Analysis in Particle Physics
  • R. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences
  • Bohm, Zech, Introduction to Statistics and Data Analysis for Physicist, free ebook
  • Blobel, Lohrmann: Statistische Methoden der Datenanlyse (in German),  free ebook
  • F. James, Statistical Methods in Experimental physics
  • W. Metzger, Statistical Methods in Data Analysisfree ebook

Practice groups

  • Group 2 (Martin Völkl)
    13 participants
    INF 227 / CIP-Pool KIP 1.401, Tue 16:00 - 18:00
  • Group 1 (Rainer Stamen)
    13 participants
    INF 227 / CIP-Pool KIP 1.401, Mon 16:00 - 18:00
Statistical Methods in Particle Physics
winter term 2021/2022
Stamen Reygers
Link zum LSF
26 participants