Advanced Multivariate Statistics

A.Y. 2021/2022
Overall hours
Learning objectives
This course is divided in two parts: (i) inference for multivariate analysis and (ii) exploratory multivariate analysis. The first part takes up the concepts of inferential multivariate statistical analysis, extending the theory about univariate inferential statistics with all the implications this extension involves. Additional topics in this context are Bayesian networks and multivariate bootstrapping. The second part will focus on exploratory multivariate analysis and will focus on further dimensional reduction techniques, correlation analysis and advanced clustering. During the course, applications to real situations will be presented using mainly the R statistical package.
Expected learning outcomes
Students will achieve skills for doing independent study and research in presence of multivariate data. Moreover, they will learn how to use dedicated R libraries to deal with multivariate contexts.
Course syllabus and organization

Single session

Lesson period
First trimester
Teaching methods.
Classes will be held on the Microsoft Teams platform both in synchronous (i.e. live) and asynchronous (i.e. recorded) mode.

Syllabus and reference material.
The syllabus and the reference material will not change in case classes will return to be held "in person".

Verification of learning and evaluation criteria.
The exam will take place with a presentation on the topic chosen using the Microsoft Teams platform or, whether the current regulations will allow it, in presence, but always in presentation form.
The exam, in particular, will be aimed at:
- ensure the achievement of objectives in terms of knowledge and understanding;
- ascertain the ability to apply knowledge and understanding through the discussion of specific cases in which topics of the course will be applied;
- verify the student's autonomy in developing an original multivariate data analysis.
Course syllabus
First part: multivariate inference
(i) Multivariate normal distributions.
(ii) Multivariate analysis of variance.
(iii) Log-linear and logistic models for categorical multivariate data.
(iv) Models for multivariate response variables
(v) Multivariate bootstrapping.
(vi) Robust multivariate analysis
(vii) Bayesian networks
Second part: exploratory multivariate data analysis
(i) Nonlinear principal component analysis
(ii) Multidimensional scaling
(iii) Multiple correspondance analysis
(iv) Canonical correlation
(v) Advanced cluster analysis
Prerequisites for admission
No mandatory prerequisites are required, but a good knowledge of statistics and probability fundamentals is strictly recommended. Matrix algebra and calculus will be beneficial but are not strictly required. Basic programming skills (especially in R) are also useful.
Teaching methods
50 percent lecture-style classes;
50 percent classroom interactive teaching activities focused on examples, case studies, research papers and applications developed mainly in R.
Teaching Resources
Lecture notes and slides of the course.
Suggested reading for insights on some topics:
Everitt, B.S., Hothorn, T. (2011). An Introduction to Applied Multivariate Analysis with R. Springer.
Everitt, B.S., Dunn, G. (2017). Applied Multivariate Data Analysis, 2nd edition. Springer.
Gifi, A. (1990). Nonlinear Multivariate Analysis. Wiley.
Härdle, W., Simar, L. ( 2007). Applied Multivariate Statistical Analysis, 2nd edition . Springer.
Assessment methods and Criteria
Some assignments will be delivered and evaluated during the course and a written final project is required. Evaluation of the project will be performed through an oral presentation and examination, in which students will be asked questions about the methods used in the project, the code produced and on the rest of the syllabus.
SECS-S/01 - STATISTICS - University credits: 6
Lessons: 40 hours
Professor: Manzi Giancarlo
Educational website(s)
Wednesday 2.30PM-5.30PM (appointment suggested, via Teams).
Room 37, 3rd Floor (due to sanitary emergency office hours in person are suspended - Office hours will be held via Teams)