Advanced Multivariate Statistics
A.Y. 2026/2027
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
Responsible
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 multivariate data analysis
· Model-based clustering
· Robust clustering
· Bootstrapping and simulation-based inference
· Multilevel models
· General-purpose computational algorithms
· Robust inference
· Exploratory multivariate data analysis
· Model-based clustering
· Robust clustering
Prerequisites for admission
A good knowledge of basic statistical and probability techniques is required. These include discrete and continuous random variables, probability distributions, descriptive statistics, regression and cluster analysis, dimensional reduction (e.g., PCA). Knowledge of linear algebra and calculus methodologies can help speed up the learning process.
Teaching methods
Classes will be composed of:
- 60% lecture-style classes
- 40% classroom interactive teaching activities focused on examples, case studies and applications developed mainly in R.
- 60% lecture-style classes
- 40% classroom interactive teaching activities focused on examples, case studies and applications developed mainly in R.
Teaching Resources
Lecture notes, slides and R code 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.
Gałecki, A., & Burzykowski, T. (2012). Linear mixed-effects model. In Linear mixed-effects models using R: a
step-by-step approach (pp. 245-273). New York, NY: Springer New York.
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.
Gałecki, A., & Burzykowski, T. (2012). Linear mixed-effects model. In Linear mixed-effects models using R: a
step-by-step approach (pp. 245-273). New York, NY: Springer New York.
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
Assessment for both attending and non-attending students will consist of an oral presentation of a project in which students apply the statistical techniques learned in class to a personal case study, formulating their own research questions.
Students will prepare a report of approximately 20 pages and an accompanying presentation. During the oral examination, they will be asked questions about the methods covered in class, the code they produced, and general topics from the rest of the syllabus.
Students will prepare a report of approximately 20 pages and an accompanying presentation. During the oral examination, they will be asked questions about the methods covered in class, the code they produced, and general topics from the rest of the syllabus.
SECS-S/01 - STATISTICS - University credits: 6
Lessons: 40 hours
Professor:
Masci Chiara
Shifts:
Turno
Professor:
Masci ChiaraProfessor(s)