This course has been designed to be useful to all physics students.

Main topics: at the end of the course, students shall be able to set up and manage many kinds of probabilistic models. Students shall obtain theoretical and operative knowledge of statistical inferential methods, with applications to data analysis in Physics. Some important statistical bases of machine learning are also taught; therefore, the students shall be able to pursue further studies in this direction.
The final exam is focused on the presentation of a topic chosen from those presented in the course, as well as on a series of codified questions that measure what has been learned. The codified questions also serve to point to the most relevant topics which constitute the heart of gravitational wave science, as well as to establish a well-determined schedule for the study of the course topics.
The resources made available to students consist of easily available textbooks and material made available by the course teacher.

1. Knowledge and understanding.
At the end of the course, the students shall be able to read advanced textbooks and scientific papers where statistical tools are applied to physical problems.
2. Applying knowledge and understanding.
At the end of the course, the students shall master the main tools of Statistics and shall be able to use them with competence in any Master thesis involving data analysis.
3. Making judgements.
At the the end of the course, the students shall be able to understand and use statistics not just in physics but also in the broader context of Big Data and Machine Learning.
4. Communication skills.
At the end of the course, the students shall know the formalism and the basic terminology of this quickly developing field.
5. Learning skills.
At the end of the course, the students shall be able to proceed on their own with the acquisition of new knowledge in the statistical field.

Mathematical methods of Physics. Basic probability and statistics.

Basic probability theory. Probability models. Probability distributions. Generating and characteristic functions. Limit theorems in probability theory. Descriptive and exploratory statistics. Monte Carlo methods. Statistical tests. Parameter estimation. Maximum likelihood method and derived methods. Statistical errors and confidence intervals. Hypothesis tests and statistical decision theory. Statistics and Machine Learning

- Handouts and scientific papers distributed during the course, and available on the course website: https://wwwusers.ts.infn.it/%7Emilotti/Didattica/StatisticaAvanzata/index.html

- A. Rotondi, P. Pedroni, and A. Pievatolo: "Probabilità, Statistica e Simulazione, 3a edizione", Springer
- Y.A. Rozanov: “Probability Theory: a Concise Course, Revised English Edition Translated and Edited by R. A. Silverman”
- G. Cowan: “Statistical Data Analysis, Oxford Science Publications

During the 2025-26 A.Y., the course topics shall be mostly the same as in the 2024-25 A.Y. They are described in detail, with a wealth of hand-outs and other teaching materials, on the course web page
https://wwwusers.ts.infn.it/~milotti/Didattica/StatisticaAvanzata/Programma_2024-25.html
This set of topics is a draft, improvements shall be implemented wherever possible.

Lectures and scientific seminars in the classroom.

For more information, please see the course website:
https://wwwusers.ts.infn.it/%7Emilotti/Didattica/StatisticaAvanzata/index.html

Short seminar (about 20 mins) on a course topic, followed by an oral examination (2 or 3 questions on the course topics). The most likely questions are listed in a special section of the course website (https://wwwusers.ts.infn.it/~milotti/Didattica/StatisticaAvanzata/Questions.html ).
The exams can be held in Italian or English, at the student's choice.

The final score shall be determined based on the correctness of the answers (more than 90% of the essential aspects correctly explained: score between 28 and 30+; between 70% and 90%, score between 24 and 27; between 50% and 70%, score between 18 and 23; less than 50%, insufficient).