Statistical Methods in Particle Physics

Learning goals and required knowledge

This course introduces basic concepts and statistical methods used in particle physics. It is a natural follow-up to the PEP4 lecture for bachelor students. Master students can attend this lecture in parallel or after the Particle Physics course.

The concepts and techniques discussed here are also applied in fields different from particle physics. 

Learning goals

• Get to know and apply the toolobx of statistical methods used in particle physics.
• Understand error bars and confidence limits 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.

Content

1. Basic concepts
2. Probability distributions
3. Uncertainty
4. Monte Carlo and numerical methods
5. Maximum likelihood estimation
6. Method of least squares
7. Goodness-of-fit and hypothesis testing
8. Confidence limits and intervals
9. Machine Learning
10. Unfolding
11. Analysis Walkthrough
12. Selected topics
    1. Kalman Filtering
    2. Symbolic Regression

Practical Information

Lecture

• Lecture will be in presence
• Thursdays: 16:15 - 17:45, KIP HS-2 (INF 227)
• First Lecture: 20. 10. 2022

Tutorials

• Tutorials will be in presence in the KIP CIP Pool
• Please register for one of the two groups
• Group 1 (Mo: 16:00 - 18:00)
• Group 2 (Tu: 16:00 - 18:00)
•  First Tutorial: 24/25. 10. 2022
• 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 notebooks on your own computer

Registration

• You need to register for one of the two groups.

Exercise Sheets

• will become available online every week after the lecture.
• can be downloaded from ths web page.
• to be handed in by Thursday 12:00 of the following week (electronically through the Übungsgruppenverwaltung).
• will be handed out as jupyter notebook.
• should be handed in as jupyter notebook as well or as pdf file (scan of handwritten solution).
• At least 60% of the points are required to qualify for the exam.

Exam

• Date: to be defined
• Format: in presence (most likely)
• will be graded. 

ECTS points

• Lecture and Tutorials: 4 ECTS points

Python

• A large fraction (>50%) of the problems consist of the implementation of statistical methods in Python in the framework of jupyter noebooks.
• A basic level of knopwledge 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.
  • 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-Sardenius: Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods
• Claude A. Pruneau: Data Analysis for Physics 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 Physicists
• Blobel, Lohrmann: Statistische Methoden der Datenanalyse
• F. James: Statistical Methods in Experimental physics
• W. Metzger: Statstical Methods in Data Analysis

Example jupyter notebooks

Error ellipse

• Plot error ellipse

Error propagation

• Gaussian error propagation with SymPy (uncorrelated variables)
• Gaussian error propagation with Sympy (correlated variables)

Machine Learning

• Simple logistic regression
• Iris data set
• MNIST softmax regression
• MNIST classification with Keras (train model, apply model)

Maximum-likelihood and least-squares fits

• Simple maximum likelihood fit
• Basic least squares fit
• Total lest-squares (errors in x and y)

Numerics, clean code

• Practical tips

Random numbers

• Random numbers from an arbitrary continous distribution
• Random numbers from multivariate Gaussian

Exercise sheets

• EX01
  
  • SMIPP_2223_01.ipynb
• EX02
  
  • SMIPP_2223_02.ipynb
• EX03
  
  • SMIPP_2223_03.ipynb
• EX04
  
  • SMIPP_2223_04.ipynb
• EX05
  
  • SMIPP_2223_05.ipynb
• EX06
  
  • SMIPP_2223_06.ipynb
• EX07
  
  • SMIPP_2223_07.ipynb
• EX08
  
  • SMIPP_2223_08.ipynb
• EX09
  
  • SMIPP_2223_09.ipynb
  • smipp_cheatsheet.zip
• EX10
  
  • SMIPP_2223_10.ipynb
• EX11
  
  • SMIPP_2223_11.ipynb

Practice groups

• Group 1 (Martin Völkl / Klaus Reygers)
  19 participants
  INF 227 1.401 CIP Pool, Mon 16:00 - 18:00