Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been  or will be  communicated to the students by the teachers, as soon as possible.
Although we do not yet know how long the social distancing related to the Covid19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been  or will be  communicated to the students by the teachers, as soon as possible.
Teacher(s)
Segers Johan; Uyttendaele Nathan (compensates Segers Johan);
Language
French
Prerequisites
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
Part 1: Basic descriptive methods and basic notations.
In this part, students are taught how matrix notation facilitates treatment of multidimensional data and basic properties of random vectors. They will also learn that the basic (uniand bivariate) descriptive tools have both their uses and limitations.
Part 2: Techniques of multivariate data analysis.
In this part, students learn about basic dimension reduction techniques for continuous and qualitative variables (principal components, correspondence analysis). Basic classification techniques are also presented. A wide range of examples is given to illustrate these methods and show when they should be used.
Part 3: Multivariate analysis models.
In this part, students see how to model intervariable relations: linear models (including variance and variancecovariance analysis) which make it possible to use explanatory variables to explain response variable variation. Models adapted to categorical response variable are also introduced, loglinear models for contingency tables, the logit model and discrimination analysis models. Here too, a wide range of examples is given to illustrate these methods and show when they should be used.
Aims
At the end of this learning unit, the student is able to :  
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”.
Content

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
Teaching methods

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.
Evaluation methods

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.
Online resources
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.
Bibliography

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.
Teaching materials
 syllabus "LINGE1222  Multivariate Statistical Analysis" (J. Segers)
Faculty or entity