# Statistical Methods in Particle Physics

winter term 2020/2021
Lecturer: Prof. Dr. Klaus Reygers (lecture), Dr. Rainer Stamen (tutorials)
36 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 helpful

## 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
• 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 hypothesis 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

## Übungsblätter

Exercise Sheets
• sheet Exercise 1
• sheet Exercise 2
• sheet Exercise 3
• sheet Exercise 4
• sheet Exercise 5
• sheet Exercise 6
• sheet Exercise 7
• sheet Exercise 8
• sheet Exercise 9
• sheet Exercise 10

## Practical Information

Lecture

• Format: flipped/inverted classroom
• Thursday meetings start at 17:00
• Lectures will be provided as videos (screencasts) and can be accessed any time. Videos are made available every week prior to the Thursday meeting (likely already on Wednesday or earlier). 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
• 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, rocket.chat, ...) are very welcome

Tutorials

• Mondays, 16:00 – 17:45 (heiCONF or Zoom)
• First tutorial: November 2, 2020
• 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

• links to the zoom/heiCONF rooms for the lecture and the tutorials will be sent to the registered participants via email prior to the first tutoral on November 2, 2020

Registration

Exercise sheets

• will be handed out every week
• to be handed in by Thursday, 10:00 of the following week

Exam

• Date: March 3rd, 2021, 9:00-11:00
• Format: Virtual exam. Problem sheet will be made available as a pdf document, you return scanned hand-written solutions.
• Writing the exam on a tablet computer with a stylus is allowed.
• You sign a form confirming that you followed the rules (e.g., no communication with others during the exam). Signing this form on a tablet computer with a stylus is allowed.
• It is permitted to consult online resources like the lecture slides, summaries of important formulas produced in the course of the lecture, or wikipedia
• Programming plays no or only a minor role for the exam
• Computer algebra programs (Mathematica, Sympy, ...) may be used. However, the problems will be such that the use of these programs is not expected to be very helpful.
• The grade for this course is the grade of the exam
• There will be a test exam an February 15/16, 2021 during the normal time of the tutorials

ECTS points

• Lecture and tutorials: 4 ECTS points

## Books

• 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

## Practice groups

Statistical Methods in Particle Physics
winter term 2020/2021
Stamen Reygers