# Fiches de cours

## Multivariate statistics

#### Enseignant(s) :

Morgenthaler Stephan

English

#### Summary

Multivariate statistics refers to data in vector form. The leading stochastic model is the multivariate Gaussian. Uncovering the associations between the components of the vectors is the main objective. The course will introduce and discuss the major types of statistical methodology.

#### Content

• the multivariate normal distribution, estimation, tests, conditional distributions
• elliptical multivariate distributions and multivariate distributions with known marginals (copulas)
• random matrices: Wishart matrices and asymptotic limits
• principal and independent components
• classification: supervised (discriminant analysis) and unsupervised (clustering) learning, machine learning
• multivariate regression and ANOVA
• canonical correlation analysis
• additional topics

#### Keywords

multivariate normal distribution, multivariate statistical methods

#### Learning Prerequisites

##### Required courses

An introductory course covering Probability Theory and Statistics

#### Learning Outcomes

By the end of the course, the student must be able to:
• Demonstrate his understanding of the course content
• Defend a data analysis he/she performed
• Critique the mis-use of multivariate statistial methods
• Justify the use of a method for a particular data set

#### Transversal skills

• Demonstrate the capacity for critical thinking
• Communicate effectively with professionals from other disciplines.
• Manage priorities.

#### Teaching methods

Classroom lectures supported by the blackboard, occasional examples shown on the beamer, exercices in class and
independent work.

#### Expected student activities

The students are expected to work in the exercise sessions and finish the exercise sheets.

Oral examination

#### Supervision

 Office hours No Assistants Yes Forum No

#### Resources

No

##### Bibliography

Consult the moodle pages of the course

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14   MAA110
14-15
15-16   MAA110
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand