Statistical Methods in Particle Physics
Learning goals and required knowledge
This course is a natural followup 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)
Content
Links to slides appear in red:

Basics concepts
 Probability
 Mean, median, mode
 Covariance and correlation
 Probability distributions

Uncertainty
 Statistical and systematic uncertainties
 Propagation of uncertainties
 Combination of uncorrelated measurements

Monte Carlo and numerical methods
 Generation of random numbers
 Monte Carlo integration
 Applications in HEP

Maximum likelihood estimation
 Basics: consistency, bias, efficiency
 Maximum likelihood method
 Method of least squares
 Goodnessoffit and hypthesis testing

Confidence limits and intervals
 Neyman construction
 FeldmanCousins confidence intervals

Machine Learning
 General Overview: machine learning, deep learning and all that
 Neural Networks
 Boosted Decision trees

Unfolding
 Response matrix
 Regularized unfolding
 "Bayesian" unfolding
A. Selected topics
Lecture videos
Week 1 (21 Oct 2020)
 01. Basic concepts, video 1 (slides 1016, 17 min)
 01. Basics concepts, video 2 (slides 1722, 18 min)
 01. Basics concepts,video 3 (slides 2328, 18 min)
 01. Basics concepts, video 4 (slides 2933, 10 min)
Week 2 (28 Oct 2021)
 01. Basic concepts, video 5 (slides 3443, 17 min)
 02. Probability distributions, video 1 (slides 19, 23 min)
 02. Probability distributions, video 2 (slides 1017, 17 min)
 02. Probability distributions, video 3 (slides 1827, 23 min)
Week 3 (4 Nov 2021)
 03. Experimental uncertainties, video 1 (slides 15, 11 min)
 03. Experimental uncertainties, video 2 (slides 612, 15 min)
 03. Experimental uncertainties, video 3 (slides 1319, 15 min)
 03. Experimental uncertainties, video 4 (slides 2024, 13 min)
 03. Experimental uncertainties, video 5 (slides 2529, 10 min)
Week 4 (11 Nov 2021)
 03. Experimental uncertainties, video 6 (slides 3039, 24 min)
 04. Monte Carlo Methods, video 1 (slides 14, 10 min)
 04. Monte Carlo Methods, video 2 (slides 59, 14 min)
 04. Monte Carlo Methods, video 3 (slides 1015, 15 min)
 04. Monte Carlo Methods, video 4 (slides 1619, 10 min)
Week 5 (18 Nov 2021)
 04. Monte Carlo Methods, video 5 (slides 2023, 9 min)
 05. Maximum likelihood estimate, video 1 (slides 16, 16 min)
 05. Maximum likelihood estimate, video 2 (slides 711, 8 min)
 05. Maximum likelihood estimate, video 3 (slides 1215, 12 min)
 05. Maximum likelihood estimate, video 4 (slides 1619, 11 min)
 05. Maximum likelihood estimate, video 5 (slides 2025, 16 min)
Week 6 (25 Nov 2021)
 05. Maximum likelihood estimate, video 6 (slides 2730, 11 min)
 05. Maximum likelihood estimate, video 7 (slides 3135, 13 min)
 06. Least squares method, video 1 (slides 15, 9 min)
 06. Least squares method, video 2 (slides 68, 9 min)
 06. Least squares method, video 3 (slides 913, 11 min)
 06. Least squares method, video 4 (slides 1416, 10 min)
 07. Hypothesis testing and goodneesoffit, video 1 (slides 17, 15 min)
Week 7 (2 Dec 2021)
 07. Hypothesis testing and goodneesoffit, video 2 (slides 815, 16 min)
 07. Hypothesis testing and goodneesoffit, video 3 (slides 1620, 14 min)
 07. Hypothesis testing and goodneesoffit, video 4 (slides 2126, 21 min)
 07. Hypothesis testing and goodneesoffit, video 5 (slides 2732, 18 min)
Week 8 (9 Dec 2021)
 08. Confidence Limits and Intervals, video 1 (slides 16, 12 min)
 08. Confidence Limits and Intervals, video 2 (slides 715, 14 min)
 08. Confidence Limits and Intervals, video 3 (slides 1622, 13 min)
 08. Confidence Limits and Intervals, video 4 (slides 2330, 11 min)
 08. Confidence Limits and Intervals, video 5 (slides 3139, 17 min)
Week 9 (16 Dec 2021)
 09. Machine Learning, video 1 (slides 17, 15 min)
 09. Machine Learning, video 2 (slides 815, 9 min)
 09. Machine Learning, video 3 (slides 1621, 11 min)
 09. Machine Learning, video 4 (slides 2228, 14 min)
 09. Machine Learning, video 5 (slides 2939, 14 min)
 09. Machine Learning, video 6 (slides 4043, 9 min)
Week 10 (13 January 2022)
 09. Machine Learning, video 7 (slides 4449, 12 min)
 09. Machine Learning, video 8 (slides 5159, 9 min)
 09. Machine Learning, video 9 (slides 6066, 11 min)
 09. Machine Learning, video 10 (slides 6774, 12 min)
 09. Machine Learning, video 11 (slides 7579, 8 min)
Week 11 (20 January 2022)
 09. Machine Learning, video 12 (slides 8087, 16 min)
 10. Unfolding, video 1 (slides 15, 8 min)
 10. Unfolding, video 2 (slides 69, 12 min)
 10. Unfolding, video 3 (slides 1013, 8 min)
 10. Unfolding, video 4 (slides 1420, 16 min)
 10. Unfolding, video 5 (slides 2129, 15 min)
Week 12 (27 January 2022)
 Selected topic 1 (Martin Völkl): Kalman filter, video 1 (slides 16, 9 min)
 Selected topic 1: Kalman filter, video 2 (slides 711, 12 min)
 Selected topic 1: Kalman filter, video 3 (slides 1217, 11 min)
 Selected topic 1: Kalman filter, video 4 (slides 1819, 5 min)
 Selected topic 1: Kalman filter, video 5 (slides 2024, 9 min)
 Selected topic 2: MNIST classification with a simple convolutional neural network using Keras
 Selected topic 3: Practical tips
Practical Information
Lecture
 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, rocket.chat, ...) are very welcome
Tutorials
 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
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 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.
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
Python
 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.
Literature
 G. Cowan, Statistical Data Analysis
 Behnke, Kroeninger, Schott, SchoernerSadenius: 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
 sheet EX01
 sheet EX02
 sheet EX03
 sheet EX04
 sheet EX05
 sheet EX06
 sheet EX07
 sheet EX08
 sheet EX09
 sheet EX10
 sheet EX11
Practice groups
 Group 2 (Martin VĂ¶lkl)
13 participants
INF 227 / CIPPool KIP 1.401, Tue 16:00  18:00  Group 1 (Rainer Stamen)
13 participants
INF 227 / CIPPool KIP 1.401, Mon 16:00  18:00
Example jupyter notebooks
Error ellipse
Error propgation
 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
 MINST classification with Keras (train model, apply model)
Maximumlikelihood and leastsquares fits
 Simple maximum likelihood fit
 Basic least squares fit
 Total leastsquares (errors in x and y)
Numerics, clean code
Random numbers