Statistical Methods in Particle Physics
Practical Information
Lecture: Thursdays 16:00 - 18:00 INF 501 / FP (R.102)
First lecture: 17.10.
Tutorial: Wednesdays 16:00 - 18:00 INF 227 / CIP-Pool KIP 1.401 (PCP)
First tutorial: 23.10.
Exercise Sheets will be handed out Thursdays and the soltutions have to be returned by Friday the following week.
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. The programming language we use is Python. Basic programming skills in python and/or C++ are advantageous but not a necessity. An introduction to the SciPy ecosystem and to the RooFit toolkit will be given. Most exercises will be provided as Jupyter notebooks that may already contain code fragments that are to be edited and completed.
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
Exercise sheets
- sheet Introduction
- sheet 1
- sheet 2
- sheet 3
- sheet 4
- sheet 5
- sheet 6
- sheet 7
- sheet 8
- sheet 9
- sheet 10
- sheet 11
- sheet 12
Practice groups
- Group G1 (Martino Borsato)
8 participants
INF 227 / SR 2.403, Wed 16:00 - 19:00