Concepts and treatment of random vectors

Teacher(s)

Kiriliouk Anna;

Language

French

Prerequisites

Concepts and tools equivalent to those taught in the UE LSTAT2014: Elements of probability and mathematical statistics

Main themes

Concepts of random vectors, multivariates moments and distributions, dependecies - preparing the student for the concept of dependence (prerequisite for many courses of the Master in Statistics)

Content

Joint probability distributions: discrete, continuous
Marginal distributions, conditional distributions
Independence
Covariance and correlation
Moments (moment generating functions) 
Conditional moments (expectation and variance)
Functions of random vectors, transformations
 Multinomial distribution
Multivariate normal distribution: construction, properties
Theory of multinormal: conditional normal, partial correlation, precision matrix, conditional independence
Other dependence concepts: copulas

Teaching methods

Lectures supplemented by practical sessions (with theoretical exercises and computer exercises).

Evaluation methods

Written exam.

Online resources

Slides on Moodle

Bibliography

Bain & Engelhardt (1992). Introduction to probability and mathematical statistics (Vol. 4). Belmont, CA: Duxbury Press.
DasGupta (2011). Probability for statistics and machine learning: fundamentals and advanced topics. New York: Springer.
Gut (2009). An Intermediate Course in Probability. Springer-Verlag (2nd edition).

Teaching materials

• Slides on Moodle

Faculty or entity

> LSBA