Multivariate statistics

Summary

Multivariate statistics focusses on inferring the joint distributional properties of several random variables, seen as random vectors, with a main focus on uncovering their underlying dependence structure. This course offers a broad introduction to its concepts, methods & theory

Content

Learning Prerequisites

Required courses

A solid introduction to probability (e.g. MATH-230) and statistics (e.g. MATH-240). Basic knowlege of linear models (e.g. MATH-341) is useful but not necessary.

Learning Outcomes

By the end of the course, the student must be able to:

• Manipulate the multivariate normal distribution and some of its extensions.
• Expound the main concepts in coupling and copulas
• Expound and apply the main dependence measures.
• Apply a canonical correlation analysis to some concrete cases.
• Apply a principal component analysis to some concrete cases.
• Perform basic multivariate hypothesis tests.
• Demonstrate a basic understanding of linear discriminant analysis.
• Demonstrate a basic understanding of graphical models theory.
• Demonstrate his/her understanding of the main mathematical concepts/proofs of the course.
• Justify the use of a method for a particular data set and objective

Teaching methods

Lecture ex cathedra using slides as well as the blackboard.

Assessment methods

Written examination.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

• Theodore W. Anderson: Multivariate Analysis, Wiley

Ressources en bibliothèque

• Multivariate Analysis / Anderson

Notes/Handbook

The slides will be available on Moodle.

Moodle Link

• https://go.epfl.ch/MATH-444