Statistical Methods in Particle Physics

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 or julia is needed (see below)

Contents

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
   • Priors
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
   • Goodness-of-fit
7. Hypothesis testing
   • Test statistics and p-values
   • Bayes factors
8. Confidence limits and intervals
   • Neyman construction
   • Feldman-Cousins confidence intervals
9. Unfolding
   • Response matrix
   • Regularized unfolding
   • "Bayesian" unfolding
10. Machine Learning
    • General Overview: machine learning, deep learning and all that
    • Neural Networks
    • Boosted Decision trees

Practical information

Lecture

• Thursday 16:15-17:45 
• First lecture: Thursday, 19 October 2023
• Lecturers: Martin Völkl (first part), Klaus Reygers (second part after Christmas)
• Slides will be made available

Tutorials

• Tutorials will be in presence in the CIP pool of Physikalisches Institut
• Mo: 16:15 - 17:45
• First tutorial: 23 October 2023
• 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

Registration

• 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 juptyer 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.

Exam

• Date: 8 February 2024, 16:10-18:10
• Place: INF 227, HS2
• Format: written exam
• The grade for this course is the grade of the exam

ECTS points

• Lecture and tutorials: 4 ECTS points

Python (or Julia)

• A large fraction (>50%) of the problems consist of the implementation of statistical methods in Python or Julia in the framework of jupyter notebooks.
• A basic level of knowledge in Python or Julia 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.
  • Python course of the lab course PAP
  • Python course at the physics department
  • Stanford Python tutorial
• 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.

Literature

• 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 Analysis, free ebook

Exercise sheets

• 01
  
  • SMIPP_2224_01.ipynb
  • SMIPP_2224_01.pdf
• 02
  
  • SMIPP_2224_02.ipynb
• 03
  
  • SMIPP_2224_03.ipynb
• 04
  
  • SMIPP_2224_04.ipynb
• 05
  
  • SMIPP_2224_05.ipynb
• 06
  
  • SMIPP_2224_06.ipynb
• 07
  
  • SMIPP_2224_07.ipynb
• 08
  
  • SMIPP_2324_08.ipynb
• 09
  
  • SMIPP_2324_09.ipynb
• 10
  
  • SMIPP_2324_10.ipynb
  • SMIPP_2324_10.pdf
  • SMIPP_10.zip
• 11
  
  • SMIPP_2324_11.ipynb

Practice groups

• Group US (Ulrich Schmidt)
  24 participants
  INF 226, CIP-Pool,1OG Süd, Raum 1.305, Mon 16:00 - 18:00