Advanced Multivariate Statistics
A.Y. 2023/2024
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.
Lesson period: First trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First trimester
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
(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
A good knowledge of basic statistical and probability techniques is required. Knowledge of linear algebra and calculus methodologies can help speed up the learning process.
Teaching methods
60% lecture-style classes;
40% classroom interactive teaching activities focused on examples, case studies, research papers and applications developed mainly in R.
40% classroom interactive teaching activities focused on examples, case studies, research papers and applications developed mainly in R.
Teaching Resources
Lecture notes and slides from 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.
Bouveyron, C., Celeux, G., Murphy, T.B., Raftery, A., E. (2019). Model-based Clustering and Classification for Data Science. Springer
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.
Bouveyron, C., Celeux, G., Murphy, T.B., Raftery, A., E. (2019). Model-based Clustering and Classification for Data Science. 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 topics from the rest of the syllabus.
Professor(s)
Reception:
Wednesday, 3PM-5PM. Starting from January 8, 2024 office hours will be ONLY by appointment and remotely via the Teams platform. Office hours on Wednesday March 6th are postponed to Thursday March 7th at 3PM
Room 37, 3rd Floor, Department of Economics, Management and Quantitative Methods.