285180 Statistical Methods for Physics Data (V) (SoSe 2024)

The aim of this lecture is to familiarise the participants with modern concepts and methods of statistics for the analysis of physical experiments and astronomical observations.

Content of the course:
- Introduction
- Probability Theory (Kolmogorov axioms, frequentist probability, Bayesian probability)
- Probability Distribution Functions (discrete PDFs, continuous PDFs, central limit theorem)
- Bayesian Approach to Probability (Bayes’ theorem, likelihood function, prior and posterior)
- Random Numbers and Monte Carlo Methods (random number generators, Markov Chain Monte Carlo)
- Parameter Estimation (estimators and their properties, maximum likelihood, chi-square test, binning of data)
- Combining Measurements (consistency of data, jack-knife, bootstrap)
- Confidence Intervalls (statistical uncertainty)
- Convolution and Unfolding
- Hypothesis Tests (statistical errors, Kolmogorov-Smirnov test, AI methods)
- Discoveries and Upper Limits (significance, systematic uncertainties, look elsewhere effect)
- Perhaps: Extreme Value Theory (distribution of extreme events)

Requirements for participation, required level

This course is recommended for students of physics starting from their third year of studies. Students from other sciences are welcome.

Bibliography

L. Lista, Statistical Methods for Data Analysis -- With Applications in Particle Physics, 3rd Edition, Springer (on-line version available via library)

Can be downloaded via
https://link.springer.com/book/10.1007/978-3-031-19934-9

F. James, Statistical Methods in Experimental Physics, 2n Edition, World Scientific

J.V. Wall & C.R. Jenkins, Practical Statistics for Astronomers, 2nd Edition, Cambridge