Laboratory of Mathematical Statistics
A.Y. 2026/2027
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.
Lesson period: Second semester
Assessment methods: Giudizio di approvazione
Assessment result: superato/non superato
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1. Descriptive statistics: introduction to the R software
2. From data to inference: confidence intervals and hypothesis testing
3. The linear regression model
3.1. Parameter estimation and inference
3.2. Regressor selection methods
3.3. Residual analysis and regression diagnostics
4. One-way and two-way ANOVA
5. Introduction to the generalized linear model: logistic and/or Poisson regression
6. Classification problems: introduction to classification trees
7. Neural networks: a brief introduction
The course will be taught with the support of the R software. For the final syllabus, please consult the course MyAriel page.
2. From data to inference: confidence intervals and hypothesis testing
3. The linear regression model
3.1. Parameter estimation and inference
3.2. Regressor selection methods
3.3. Residual analysis and regression diagnostics
4. One-way and two-way ANOVA
5. Introduction to the generalized linear model: logistic and/or Poisson regression
6. Classification problems: introduction to classification trees
7. Neural networks: a brief introduction
The course will be taught with the support of the R software. For the final syllabus, please consult the course MyAriel page.
Prerequisites for admission
A basic course of Probability and Mathematical Statistics
Teaching methods
Computer lab sessions and interactive lectures.
Teaching Resources
- V. Capasso, D. Morale, Una Guida allo studio della Probabilità e della Statistica Matematica, Esculapio editore
- G.G. Roussas, A Course in Mathematical Statistics, Academic Press
- N. Draper, H. Smith, Applied Regression Analysis, Ultima Edizione
- P.K.Dunn, G.K.Smyth, Generalized linear models with examples in R, Springer, 2018 (disponibile nella biblioteca digitale di UniMI)
- G.G. Roussas, A Course in Mathematical Statistics, Academic Press
- N. Draper, H. Smith, Applied Regression Analysis, Ultima Edizione
- P.K.Dunn, G.K.Smyth, Generalized linear models with examples in R, Springer, 2018 (disponibile nella biblioteca digitale di UniMI)
Assessment methods and Criteria
The exam consists of submitting a set of homework assignments that will be assigned by the instructors during the course. These assignments involve solving problems requiring specific statistical analyses. Completing the homework requires attending the course in real time; therefore, attendance is strongly recommended.
Non-attending students will be required to take an oral exam covering the entire course syllabus and ad hoc homework assignments.
The assessment will evaluate the student's ability to analyze and draw conclusions from the analyses performed. The grading will be Pass / Fail.
Non-attending students will be required to take an oral exam covering the entire course syllabus and ad hoc homework assignments.
The assessment will evaluate the student's ability to analyze and draw conclusions from the analyses performed. The grading will be Pass / Fail.
MATH-03/B - Probability and Mathematical Statistics - University credits: 3
Laboratories: 36 hours
Professors:
Morale Daniela, Ugolini Stefania
Professor(s)
Reception:
Please write an email
Room of the teacher or online room