Statistical models advanced course

Course objectives

Learning goals. The aim of this course is to increase the knowledge of multivariate statistical models for analyzing and understanding complex (often very large) data matrices. Students have to be able to formalize the real problems in terms of the models discussed during the course and to interpret the obtained results. Finally, students have to program and apply these methodologies by using statistical software (in particular R / Matlab). Knowledge and understanding. After attending the course, students know and understand the main multivariate statistical models to deal with the studies of complex phenomena. Applying knowledge and understanding. At the end of the course, students are able to use and select among several multivariate statistical models to face problems related to different fields. Students are able to critically interpret the results obtained on real data sets by using statistical software (in particular R / Matlab). Making judgements. Students develop critical skills through the application of statistical models on real data and the comparison among solutions obtained from different models aimed at facing the same problem. Communication skills. Students, through practical exercises, reading and critical evaluation of scientific papers and group activities, acquire the technical-scientific ability to communicate results obtained on real problems. Learning skills. At the end of the course, students have a broader knowledge of the multivariate statistical models that allow them to carry out complex analysis strategies to extract the relevant information from the observed data, often of large size. This prerogative, combined with the knowledge of programming statistical software, responds to the increasing requests of the market (companies, research institutions, etc.).

Channel 1
FRANCESCA MARTELLA Lecturers' profile

Program - Frequency - Exams

Course program
The lectures are divided into the following thematic areas: PART 1 (about 18 hours) • Recall the rules of matrix algebra • Clustering Methodologies: o Recall the distance-based methodologies o Model-based methodologies (in particular based on finite mixture models) PART 2 (about 30 hours) • Extensione of finite mixture models • Methodologies of clustering for units and dimensional reduction of variables • Methodologies of clustering for units and variables PART 3 (about 24 hours) Applications on real data set by using Statistical software (R/Matlab) and discussion of scientific papers.
Prerequisites
To deal with the course content, a basic knowledge of matrix algebra, theory of statistical inference, linear regression model, mathematical analysis is required.
Books
- Lecture notes and scientific papers given by the Professor during the course. - An introduction to clustering with R, Springer. Giordani P., Ferraro M.B., Martella F. (2020) - Finite Mixture Models, Wiley Series in Probability and Statistics. McLachlan G. and Peel D. (2000) - Methods of Multivariate Analysis, Wiley Series in Probability and Statistics (2nd edition). Rencher A.C. (2002)
Teaching mode
The frontal lectures (unless health emergencies) are organized by alternating theoretical lectures, use of software for applications on real data sets and working groups.
Frequency
Participation at lectures is strongly encouraged. If it is not possible, please contact the Professor.
Exam mode
In order to pass the exam, students have to: (a) Make a lab exam where multivariate statistical models have to be applied on one or more real data sets by using software discussed during the course; (b) make a team work (planned with the Professor): critical presentation of a scientific paper given by the Professor. If a student is not attending the frontal lectures, it is recommended to contact the Professor; (c) make an oral exam to evaluate the knowledge and understanding of the discussed methods. Each part of the exam is worth 1/3 of the final vote.
Bibliography
- G. McLachlan, D. Peel, (2000). Finite Mixture Models, Wiley Series in Probability and Statistics. - A.C. Rencher, (2002). Methods of Multivariate Analysis, Wiley Series in Probability and Statistics; 2nd edition. - A.D. Gordon (1999). Classification, Chapman & Hall, 2nd edition. - P. Giordani, Ferraro M.B., Martella F. (2020) An Introduction to Clustering with R. Springer Singapore.
Lesson mode
The frontal lectures (unless health emergencies) are organized by alternating theoretical lectures, use of software for applications on real data sets and working groups.
  • Lesson code10589781
  • Academic year2024/2025
  • CourseStatistical Sciences
  • CurriculumDemografico sociale
  • Year2nd year
  • Semester1st semester
  • SSDSECS-S/01
  • CFU9
  • Subject areaStatistico