Laboratory of Mathematical Statistics

A.Y. 2021/2022
3
Max ECTS
36
Overall hours
SSD
MAT/06
Language
Italian
Learning objectives
The course aims to aware students to the theoretical and computational aspects of first statistical tools, by analyzing simulated and real data sets. We introduce and use R software, which is the state-of-art in scientific community and widely used in many industrial and commercial environments. Students will link mathematical theory and its application in modelling instances. Thy will improve their computing and computer science abilities as well as his probem solviving attitudes.
Expected learning outcomes
The student shall be able to perform a statistical analysis of data from different working contexts using the R package. He shall have acquired the ability to use basic R tools and to resume relevant information from the available data. Students become conscious of the role of mathematical theory in algorithms development.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
in the case of lockdown, in addition to Teams, students are required to have statistical software installed on his/her personal PC (R). Tutorial on Ariel on how to install it. More specific information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation.
Course syllabus
1. Introduction to statistical software (SAS or R)
2. Introduction to GLM (General Linear Models): general formulation, link function
3. Case in which the link function is the identity: linear regression model.
3.1. Parameters estimates
3.2. Methods for variable selection
3.3. Residual analysis and regression diagnostics
4. Presence of dummy variables
5. One way and two ways ANOVA
6. Link function as logit: logistic regression
7. Classification and regression trees (CART)
8. Introduction to neural networks (if enough time)
Prerequisites for admission
The content of the course Mathematical Statistics (ex CPSM2) is strongly recommended for an in-depth understanding
Teaching methods
computer lab lessons
Teaching Resources
· Peter K. Dunn · Gordon K. Smyth, Generalized Linear Models With Examples in R, Springer Texts in Statistics, 2018
· G.G. Roussas, A Course in Mathematical Statistics, Academic Press, 1997 (or more recent editions)
· A.Agresti, Categorical data analysis, Wiley, 2nd edition (2002)
· N. Draper, H. Smith, Applied Regression Analysis, Last Edition
· A.J.Izenman, Modern multivariate statistical techniques.. Regression, classification, and manifold learning, Springer, 2008
Assessment methods and Criteria
Written exam in lab (PC based exercises)
MAT/06 - PROBABILITY AND STATISTICS - University credits: 3
Laboratories: 36 hours
Professor(s)
Reception:
on appointment
office 2099
Reception:
Appointment by email
Office or online (by videocall)