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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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