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STAT-F600
Multivariate and high-dimensional statistics
Course teacher(s)
Thomas VERDEBOUT (Coordinator)ECTS credits
5
Language(s) of instruction
english
Course content
In the first part of the course we review some basic statistical concepts in point estimation and hypothesis testing. Then we properly define the multivariate Gaussian distribution and present some classical Multivariate Methods of inference for this model including the Hotelling test and the sphericity test. Then we discuss the general linear model and present some classical multivariate methods such as Principal Component Analysis and Discriminant analysis. The last part of the course is dedicated to the extension of these various methods to the high-dimensional situations where the number of observed variables may be as big or bigger than the number of observations.
Objectives (and/or specific learning outcomes)
The main objective of this course is to provide the more recent methodologies in statistics that offer the possibilty to deal with "big data". More precisely, we show how inference can be performed when both the number of observations and the number of observed variables are big. We start the course by reviewing some classical Multivariate Methods and show how they can be adapted to deal with such massive data sets. At the end of this UE, the student will be able to determine a correct methodology to deal with multidimensional data and to use R to implement it. She/he will be able to use methods that are adapted to large databases.
Teaching methods and learning activities
Mainly based on oral presentations with slides. We also propose a group project related to the last part of the course.
Contribution to the teaching profile
Please see the French part.
References, bibliography, and recommended reading
1) Theory of Multivariate Statistics, Bilodeau and Brenner, 1999, Springer 2) Statistics for High-dimensional data, Buhlmann and van de Geer, 2011, Springer
Course notes
- Podcast
Other information
Contacts
Thomas Verdebout (thomas.verdebout@ulb.be)
Campus
Plaine
Evaluation
Method(s) of evaluation
- written examination
- Project
- Other
written examination
Project
Other
Written exam and group project.
Mark calculation method (including weighting of intermediary marks)
The final grade is obtained by a weighted combination of two grades: the group project (with weight 30%) and the written exam with weight (70%).
Language(s) of evaluation
- english