Statistical Methods in Particle Physics

Announcements

Exam: 

The exam will take place on February 12th, 2019 at 14:00 in the small lecture Hall kHS, Philosophenweg 12.

Both the lecture  and tutorial have been moved to start at 16:15h in order to avoid a collission with the Particle Physics lecture!

Learning goals

Successful participants will have a working knowledge of the application of statistics to typical problems in particle physics, from detector physics to the analysis of differential cross sections and the search for new particles. They will be able to understand the process of making a measurement and how the inferred results are typically reported in publications. They can interpret statistical uncertainties and confidence limits and will be able to apply basic techniques for their calculation to their own problems. Additional material on algorithms needed to reconstruct the data recorded by partical physics experiments, to select and classify data sets and an introduction to machine learning will enable them to follow the modern literature on these issues.

Prerequisits

The lecture assumes a basic understanding of experimental particle physics (as taught in the bachelor course).

The main tool of data analysis is the computer. Therefore the exercises will contain programming assignments. An introduction to ROOT, the main data analysis framework used by particle physicists, will be provided. Basic programming skills in C++ and/or python are advantageous but not a necessity.

Contents

Fundamentals

• Statistics in high energy phsics
• Probabilities
• What type of problems can be answered with statistical methods?
• Bayesian and Frequentist statistics

Probability densities

• Random variables
• Probability density functions
• Mean, covariance, moments
• Probabilities in n dimensions
• Uncertainties and error propagation
• Monte Carlo algorithms

Parameter Estimation

• Estimators, bias, variance
• Maximum likelihood method

Hypothesis Testing

• Power and significance level
• Nyman-Pearson Lemma

Confidence Intervals

• The Neyman construction
• Intervals and Limits
• Sensitivity

Special lecture: From raw data to results, event reconstruction in partical physics

• The Kalman filter

Introduction to machine learning in particle physics

• Supervised learning
• Classification
• Ensemble learning

Material

• SMIPP2018_Intro.pdf
• smipp18_script.pdf
• smipp18_slides.pdf

Practical Information

• The lecture takes place on Tuesdays, 16:15h in INF 227 / SR 3.402
• The first lecture will be given on October 16th
• Exercises will be held Thursday afternoon 16:15h-17:45h in the KIP computer room

Exercise sheets

• 1
  
  • SMIPP_Exercise_01.pdf
• 2
  
  • SMIPP_Exercise02.pdf
  • exercise_02_3.root
• 10
  
  • SMIPP_Exercise10.pdf
• 11
  
  • SMIPP_Exercise11.pdf
• 12
  
  • SMIPP_Exercise12.pdf
• 3
  
  • exercise_3_3.txt
  • SMIPP_Exercise03.pdf
• 4
  
  • SMIPP_Exercise04.pdf
• 5
  
  • SMIPP_Exercise05.pdf
  • data_05.h
• 6
  
  • SMIPP_Exercise06.pdf
• 7
  
  • SMIPP_Exercise07.pdf
  • exercise07.root
  • Exercise_07_2_start.C
• 8
  
  • SMIPP_Exercise08.pdf
• 9
  
  • SMIPP_Exercise09.pdf
  • exercise09.txt

Practice groups

• Group Exe (Pizzella, Veronica)
  10 participants
  INF 227 / CIP-Pool KIP 1.401, Thu 14:00 - 17:00