Random vectors: modelling and processing

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

The course prepares students for the concepts of dependence via random vectors, multivariate and conditional distributions, covariance and correlation, multivariate normal distribution, and copulas.  

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