The course aims to provide an introduction to the problems and methods of classical statistical inference.
KNOWLEDGE AND UNDERSTANDING.
At the end of the course the student will have to prove that he has acquired the knowledge of some complementary topics of probability theory necessary to deal with the formal aspects of statistical inference procedures, with specific regard to the main families of parametric distributions, and will have to master and understand the basic principles of statistical inference and its fundamental tools.
APPLYING KNOWLEDGE AND UNDERSTANDING.
At the end of the course, the student should be able to solve simple theoretical problems and be able to go over the proofs of some remarkable results; he will also have to be able to deal with problems related to the estimation and testing of hypotheses in some simple situations.
MAKING JUDGEMENTS.
The student will have to show that he is able to critically and appropriately choose the inferential technique to be used in concrete cases.
COMMUNICATION SKILLS.
The student must be able to communicate the main ideas and fundamental theorems of statistical inference in a clear and formally correct way.
LEARNING SKILLS
The student must be able to independently explore some topics and learn the use of tools that are simple extensions of the techniques illustrated in the course.

Students should have a knowledge of elements of calculus, probability theory and exploratory data analysis.
The following courses are prerequisites for the Statistical Inference course: Matematica per l'economia e la statistica 1; Calcolo delle probabilità; Analisi esplorativa dei dati.

1. Introduction to statistical inference
2. Fundamentals of probability theory. Random variables (r.v.s) and parametric families of distributions for discrete and continuous variables. Transformations and linear combinations of r.v.s. Successions of r.v.s and convergence. Law of large numbers and central limit theorem.
3. Statistical Inference
(a) Introduction to classical problems in statistical inference: parametric and nonparametric approach. Statistics and sampling distributions. The Chi-square, Student t and Fisher's F distributions.
(b) Point and interval estimation. Properties of estimators and methods for finding and evaluating estimators. Maximum likelihood estimators and their properties. Some important examples. A brief discussion on the Bayesian approach to statistical inference.
(c) Hypothesis testing and significance tests. The Neyman-Pearson approach. Examples. Nonparametric tests.

- N. Torelli, R. Pappadà: Richiami e Complementi
di Calcolo delle Probabilità, & Elementi di inferenza statistica (vol.1 e 2). Available on the Moodle page of the course
- Pauli F., Torelli N., Trevisani M., Statistica: esercizi ed esempi, Pearson Education, Milano (2007)
- other materials presented in class and made available on the Moodle page of the course

The course takes place through lectures which include the development of theoretical topics, exercises and guided examples and a cycle of practical exercises, some of which conducted with the aid of the software R. The active involvement of students in the classroom is encouraged, where students are called to intervene by asking and/or answering questions; several theoretical and practical homework to be submitted within a given deadline are assigned throughout the course.

Any other information will be provided on the course website and on the course team.
The lessons will be recorded, in accordance with the decisions made by the academic bodies. Recordings will not be made for laboratory lessons which require the active intervention of the students. Students of the Artificial Intelligence and Data Analytics degree course who change their course are expected to carry out support activities entrusted to a tutor.

The exam consists of a written test (2 hours, 4 exercises which comprise 3 to 4 specific questions) in which the student is asked to correctly apply the methods of inference to solve problems similar to those carried out in class. Those who pass the written test with a minimum score of 15/30 are admitted to an oral exam.
The oral exam covers the entire program of the course.
The written test aims to verify the student's ability to apply the knowledge acquired. The oral exam aims to evaluate the understanding of some of the most relevant topics, the ability to retrace some notable demonstrations, critical thinking, and the ability to recognize the validity of the assumptions underlying some of the illustrated methodologies.
The final grade is a weighted average of the grade obtained in the two parts (with a weight of 0.7 in the oral exam and 0.3 in the written test). To pass the exam the student must obtain an evaluation of at least 18/30.

This course covers some topics related to one or more objectives of the 2030 Agenda for the Sustainable Development of United Nations.