 1 This course develops the elements introduced in the basic Probability and Statistics courses within a multivariate framework, the aim being to equip students with the instruments they need to analyse multidimensional data sets. By the end of the course, students should be able to use the most widelyused instruments to analyse real data. A key aim of the course will therefore be to give students a clear understanding of the methods and how to apply them, and how to use relevant analytical software.
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

Introduction to multivariate data analyis

Linear algebra and Euclidean geometry

Descriptive statistics for data matrices

Principal component analysis

Cluster analysis: kmeans clustering and hierarchical cluster algorithms

Linear discriminant analysis

Distribution theory

Multiple linear regression, including AN(C)OVA

Logistic regression

Lectures: the teacher introduces the concepts through an application and then presents the abstract form

Exercise sessions in computer rooms: the teacher gives students realdata problems to solve using the statistical software environment R.

Computer test: at the end of the course, the students need to solve multiple choice questions related to real data sets, to be solved using the statistical software environment R. This part is openbook.

Exam: written, closed book, with the help of a formula list and a pocket calculator. The exam part comprises both theory questions as well as exercises related to interpreting and reconstructing the output of the R software.
The list of formulas, the slides used in the lectures and the computer labs, R software documentation and links to external web resources (videos, online courses, documents) are available on the MoodleUCL course page.
 syllabus "LINGE1222  Multivariate Statistical Analysis" (J. Segers)

Härdle, W. and L. Simar (2007): Applied Multivariate Statistical Analysis, 2nd Edition, SpringerVerlag, Berlin.

James, G., Witten, D., Hastie, T. and R. Tibshirani (2013): An Introduction to Statistical Learning, Springer, New York.

Saporta, G. (2011): Probabilités, analyse des données et statistique, 3e édition révisée, Editions TECHNIP, Paris.