Advanced multivariate statistics
A.A. 2022/2023
Obiettivi formativi
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.
Risultati apprendimento attesi
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.
Periodo: Primo trimestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento non può essere seguito come corso singolo. Puoi trovare gli insegnamenti disponibili consultando il catalogo corsi singoli.
Programma e organizzazione didattica
Edizione unica
Periodo
Primo trimestre
Teaching methods.
Classes will be held on the Microsoft Teams platform both in synchronous (i.e. live) and asynchronous (i.e. recorded) mode.
Classes will be held on the Microsoft Teams platform both in synchronous (i.e. live) and asynchronous (i.e. recorded) mode.
Programma
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
Prerequisiti
No compulsory prerequisites are required, but a good knowledge of basic statistics and probability is strongly recommended. Matrix algebra and calculus will be beneficial but are not strictly required. Basic programming skills (especially in R) are also useful.
Metodi didattici
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.
Materiale di riferimento
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
Modalità di verifica dell’apprendimento e criteri di valutazione
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.
SECS-S/01 - STATISTICA - CFU: 6
Lezioni: 40 ore
Docente:
Manzi Giancarlo