Statistical Methods in Particle Physics
Wintersemester 2020/2021
Dozent: Prof. Dr. Klaus Reygers (lecture), Dr. Rainer Stamen (tutorials)
Link zum LSF
36 Teilnehmer/innen
Dozent: Prof. Dr. Klaus Reygers (lecture), Dr. Rainer Stamen (tutorials)
Link zum LSF
36 Teilnehmer/innen
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 helpful
Contents
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 hypothesis 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 (5 Nov 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 (12 Nov 2020)
 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 (19 Nov 2020)
 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 (26 Nov 2020)
 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 (3 Dez 2020)
 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 (10 Dez 2020)
 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 (17 Dez 2020)
 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 (14 January 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 (21 January 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 (28 January 2021)
 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 (4 February 2021)
 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 (11 February 2021)
 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
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
Zoom/heiCONF links
 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
 You need to register for this course
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, 9:0011:00
 Format: Virtual exam. Problem sheet will be made available as a pdf document, you return scanned handwritten 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, 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
Übungsgruppen
 Gruppe 1 (Rainer Stamen)
18 Teilnehmer/innen
Mo 16:00  18:00  Gruppe 2 (Martin Völkl)
18 Teilnehmer/innen
Di 16:00  18:00
Example jupyter notebooks
 Plot 2d Gaussian
 Plot error ellipse
 pvalues and number of standard deviations
 Unknownsided dice example
 Gaussian error propagation with SymPy (uncorrelated variables)
 Gaussian error propagation with SymPy (correlated variables)
 Random numbers from multivariate Gaussian
 Random numbers from an arbitrary continous distribution
 Unbinned maximum likelihood fit with iminuit from the lecture
 Extended unbinned maximum likelihood fit with iminuit from the lecture
 Basic χ^{2} fit
 Total least squares (fit with errors in both x and y)
 Simple logistic regression example
 Classification example: the iris data set
 MNIST softmax regression
 MNIST classification with a convolutional neurel network using Keras (train model)
 MNIST classification with a convolutional neural network using Keras (apply model)
 Practical tips