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
- Random vectors and random matrices.
- Product moments and covariance Matrices.
- The multivariate Gaussian and elliptical distributions.
- Limit theorems and concentration of measure.
- Coupling and copulas, measures of dependence
- PCA, CCA, and LDA.
- Covariance estimation and hypothesis testing.
- Nonparametric and semiparametric estimation.
- Gaussian graphical models and conditional independence
- Multivariate statistics in high dimensions.
- Introduction to functional data analysis.
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
Office hours | No |
Assistants | Yes |
Forum | Yes |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
- Theodore W. Anderson: Multivariate Analysis, Wiley
Ressources en bibliothèque
Notes/Handbook
The slides will be available on Moodle.
Moodle Link
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: obligatoire
- Semestre: Printemps
- Forme de l'examen: Ecrit (session d'été)
- Matière examinée: Multivariate statistics
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: obligatoire
Semaine de référence
Lu | Ma | Me | Je | Ve | |
8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Légendes:
Cours
Exercice, TP
Projet, labo, autre