Multivariate Verfahren / Summer semester 2024

In this course, we will embark on an exploration of central topics in multivariate statistics. As the class is intended for advanced Bachelor's or early Master's students, it is likely that you have heard about or studied several of these topics before - however, my aim is to provide a fresh and more fundamental perspective on these concepts, fostering a deeper understanding and encouraging you to learn how to approach multivariate statistics from different angles.

Specifically, we will focus on the two following perspectives that may be used, sometimes in combination, to frame all statistical methods covered in this course:

• Geometric/Algebraic i.e. based on Linear Algebra
• Probabilistic, i.e. based on Probability Theory

Topics covered in this course:

1. Basics of probability theory
2. Basics of linear algebra
3. Multivariate Data Types and Descriptive Statistics
4. Multivariate Distributions
5. Distance and Similarity Measures
6. Supervised Learning
6.1 Multivariate Regression
6.2 Classification Methods
7. Unsupervised Learning
7.1 Clustering
7.2 Dimensionality Reduction: a Motivation
7.3 Principal Component Analysis (PCA)
7.4 Multidimensional Scaling (MDS)
8. Applications and Case studies in R

The goal is that after completing this course, you will have

• developed a solid framework with which to approach the comprehension of statistical methods that are new to you
• understood the purpose of employing probabilistic methods in statistical modelling - specifically when, how, and why this is necessary or beneficial.

This class may be completed either as a 6CP course, for which you will need to only pass the final exam, or as a 9CP course, for which you will need to additionally complete the final project.

All further information on grading and the modalities of the final exam will be given on the moodle page for this course.

For any Questions or feedback you may contact me anytime under hannah.kuempel@ibe.med.uni-muenchen.de. Additionally, the moodle page provides an interactive forum for this class as well as the option to pose questions and give feedback anonymously.