# Statistical Methods in Particle Physics

winter term 2017/2018
Lecturer: Prof. Dr. Klaus Reygers
27 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

## Contents

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. Parameter estimation
• Basics: consistency, bias, efficiency
• Maximum likelihood method
• The method of least squares
6. Hypothesis testing
• Neyman-Pearson lemma
• p-value
• Look-Elsewhere effect
7. Confidence limits and intervals
• Neyman construction
• Feldman-Cousins confidence intervals
8. Multivariate analysis
• Fisher linear discriminnat
• Neural Networks
• Boosted Decision trees
9. Unfolding
• Response matrix
• Regularized unfolding
• "Bayesian" unfolding

## News

• "Klausureinsicht" on 14 February 2018 from 10:00am - 11:00am in INF 227 (KIP) / SR 3.404
• Date of written exam: 5 February 2018 (2:15pm - 4:15pm), more details further below

## Required knowledge

On the statistics side, there is no special knowledge is requires, and we will (briefly) repeat the basic principles of statistics. On the particle physics side, the PEP4 lecture is sufficient, and the lecture can serve as a natural follow-up of PEP4 for Bachelor students interested in Particle Physics. Master students are invited to attend this lecture in parallel or after the Particle Physics course. The tutorials will provide a step-by-step introduction to root and some basics of C++.

## Practical information

Lecture

• Mondays 14:15 – 15:45 in INF 227 (KIP) / SR 3.404. Exception: first lecture (on 16 Oct 2017) starts at 15:00!
• First lecture: October 16, 2017

Tutorials

Exercise sheets

• will be handed out every week
• solutions have to handed in by email

Exam

• A written exam will take place on 5 February 2018, 14:15–16:15 in KIP, HS1
• You can bring one DIN A4 sheet with formulas etc. (you can use both sides)
• A pocket calculator is needed. Please bring one.

ECTS points

• Lecture and tutorials: 4 ECTS points

• Tutorial 1
• Tutorial 2
• Tutorial 3
• Tutorial 4
• Tutorial 5
• Tutorial 6
• Tutorial 7
• Tutorial 8
• Tutorial 9

## Contact

Statistical Methods in Particle Physics
winter term 2017/2018
Reygers