Advanced Multivariate Statistics
A.Y. 2025/2026
Learning objectives
The course is designed to teach cutting-edge statistical methods for analyzing multivariate data. Its central theme is inspired by the paper Gelman, A., & Vehtari, A. (2021). What are the most important statistical ideas of the past 50 years? Journal of the American Statistical Association, 116(536), 2087-2097. During the course, applications to real situations will be presented using the R statistical software.
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: Second four month period
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
Lesson period
Second four month period
Course syllabus
The course is designed to teach cutting-edge statistical methods for analyzing multivariate data. Its central theme is inspired by the paper Gelman, A., & Vehtari, A. (2021). What are the most important statistical ideas of the past 50 years? Journal of the American Statistical Association, 116(536), 2087-2097. The course covers the following topics:
· Bootstrapping and simulation-based inference
· Multilevel models
· General-purpose computational algorithms
· Robust inference
· Exploratory data analysis
· Model-based clustering
· Robust clustering
· Bootstrapping and simulation-based inference
· Multilevel models
· General-purpose computational algorithms
· Robust inference
· Exploratory data analysis
· Model-based clustering
· Robust clustering
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.
Everitt, B., & Hothorn, T. (2011). An introduction to applied
multivariate analysis with R. Springer Science & Business
Media.
Tibshirani, R. J., & Efron, B. (1993). An introduction to the
bootstrap. Monographs on statistics and applied
probability, 57(1), 1-436.
Maronna, R. A., Martin, R. D., Yohai, V. J., & Salibián-Barrera,
M. (2019). Robust statistics: theory and methods (with R).
John Wiley & Sons.
Pinheiro, J., & Bates, D. (2006). Mixed-effects models in S
and S-PLUS. Springer science & business media.
Bouveyron, C., Celeux, G., Murphy, T. B., & Raftery, A. E.
(2019). Model-based clustering and classification for data
science: with applications in R (Vol. 50). Cambridge
University Press.
Everitt, B., & Hothorn, T. (2011). An introduction to applied
multivariate analysis with R. Springer Science & Business
Media.
Tibshirani, R. J., & Efron, B. (1993). An introduction to the
bootstrap. Monographs on statistics and applied
probability, 57(1), 1-436.
Maronna, R. A., Martin, R. D., Yohai, V. J., & Salibián-Barrera,
M. (2019). Robust statistics: theory and methods (with R).
John Wiley & Sons.
Pinheiro, J., & Bates, D. (2006). Mixed-effects models in S
and S-PLUS. Springer science & business media.
Bouveyron, C., Celeux, G., Murphy, T. B., & Raftery, A. E.
(2019). Model-based clustering and classification for data
science: with applications in R (Vol. 50). Cambridge
University Press.
Assessment methods and Criteria
Evaluation will be performed through an oral presentation of a project, in which students will be asked questions about the methods learned in class, the code produced and general topics from the rest of the syllabus.
SECS-S/01 - STATISTICS - University credits: 6
Lessons: 40 hours