Statistical Methods and Applications

ROBERTO ROCCI
ROBERTO ROCCI

Educational objectives
The educational goal of the course is students' learning of the fundamentals of probability calculus and statistical inference.

Knowledge and understanding
At the end of the course, students know and understand how to formalize the uncertainty and how to make inference about unknown parameters.

Ability to apply knowledge and understanding
Students learn how to formalize a problem in the field of probability calculus or statistical inference.

Judgment independence
The discussion of the various methods, even with team works, provides students with the skills necessary to analyze real situations critically and independently.

Communicative skills
Students acquire the basic elements for reasoning in quantitative terms about uncertainty and inference problems.

Learning skills
Students who pass the exam are able to apply the methods learned in different application contexts.

The aim of the course is to teach statistical reasoning through the main notions of probability calculus and statistical inference.

No preliminary exams.
However, it is necessary to know the fundamentals of calculus and descriptive statistics.

Week Probability
1-2 Definition of probability. Basic concepts and rules
3 Discrete random variables (r.v.s)
4 Continuous r.v.s
5 Multivariate r.v.s
6 Sequences of r.v.s

Statistics
7-8 Statistical model
9-10 Point estimation
11 Confidence intervals
12 Tests

- D. P. Bertsekas, J. N. Tsitsiklis (2008). Introduction to Probability, 2nd edition. Athena Scientific.
- G. Casella, R. L. Berger (2002). Statistical inference. Pacific Grove, CA: Duxbury. Thomson Learning.
- Slides and Exercises by the teacher.

- K. Knight (2000). Mathematical statistics. Chapman & Hall/CRC.

Theoretical lessons, discussions of exercises and applications on real data.
Whenever possible, all the activities will be carried out in class.

Students are strongly encouraged to attend the lessons.

The final exam is in two parts: written (80%) with exercises and theoretical questions, with open and close answer, oral (20%).
The written part can be taken during the course with some intermediate tests.

See the materials on the Moodle website