# GRK 2149 workshop: Statistical Methods in Particle Physics

Lectures for the Retreat of the Research Training Group (Graduiertenkolleg) 2149 "Strong and Weak Interactions" - 9-10 September 2020

## Overview

• Basics
• Maximum likelihood method
• Least Squares
• Hypothesis tests and Goodness-of-fit
• Systematic uncertainties
• Decision trees

We'll use python 3 in the course. Basic knowdegle of the language is useful for this course. We'll work a lot with jupyter notebooks. A nice summary of important python commands is available on the website of the Stanford lecture CS231n.

Here you find the slides of the lecture.

## Problems

1. Construct a Bayesian credible interval (html, notebook) ⧖ [solution: html, notebook]
2. Unbinned maximum likelihood fit (double exponential decay) (html, notebook) ⧖⧖ [solution: html, notebook]
3. The lighthouse problem: another unbinned maximum likelihood fit (html, notebook) ⧖⧖ [solution: html, notebook]
4. Unbinned maximum likelihood fit with Gaussian constraint on a parameter (html, notebook) ⧖ [solution: html, notebook]
5. Linear least squares and error propgation (html, notebook) ⧖⧖ [solution: html, notebook]
6. Simultaneous least-squares fit to several data sets (blast-wave fit to particle spectra) (html, notebook) ⧖⧖⧖ [solution: html, notebook]
7. Kolmogorov-Smirnov test (html, notebook) ⧖ [solution: html, notebook]
8. Significance of a peak above background (html, notebook) ⧖⧖⧖ [solution: html, notebook]
9. Least-squares fit with external Gaussian constraint (html, notebook) ⧖ [solution: html, notebook]
10. Separation of gamma and hadron showers measured with the MAGIC Cherenkov telescope using a boosted decision tree and a random forest (html, notebook) ⧖⧖ [solution: html, notebook]
⧖ = quick, ⧖⧖ = intermediate, ⧖⧖⧖ = takes a bit longer

Download zipped tar file with data and jupyter notebooks (unpack with `tar xvzf notebooks_and_data.tgz`).
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