Probability and statistics

A.Y. 2020/2021
Overall hours
FIS/03 FIS/04
Learning objectives
The course is meant to provide the student with a deep knowledge of probability theory and with the statistical methods on which physics and data modelling are grounded. Besides giving the definitions and the concepts of frequentist and Bayesian interpretation of probability, operative tools will be discussed, such as the law of large numbers, the central limit theorem, the use of generating functions and the principle of maximum entropy.
Expected learning outcomes
The student will be able to use the concepts of probability theory to analyse data, make statistical inference and statistical tests. Moreover, they will be confident with the theoretical bases of statistical mechanics and with its tools.
Course syllabus and organization

Single session

Lesson period
First semester
Classes will take place on Zoom. Breakout rooms will be used for group exercises. The lessons will be carried out in synchronous mode and recorded. The recordings will be available on Ariel. The computational exercises will be available on github and conducted on web interface (binder). Whenever possible, platforms for online exercises and surveys will be used.
Course syllabus
Elements of probability theory:
The definition of probability: frequent and Bayesian approach
Conditional probability
Average, moments, standard deviation, generating function
Random discrete variables
- Combinatorics calculation
- Binomial and multinomial distributions
- Occupation numbers
- Law of large numbers
- Poisson processes
Continuous distributions
- probability density
- cumulated distributions
- characteristic functions
- examples: Uniform, Gaussian, Exponential, Beta, Gamma, etc.
Extreme-value and rank statistics
Sum statistics. Central limit, stable distributions
Principle of maximum entropy

Statistical estimates:
Confidence intervals
Maximal likelyhood

Statistical tests:
The design of an experiment
statistical significance
P-value: T-test, F-test, KS-test

Statistical visualization:
Univariate distributions: histograms, boxplot, swarmplot
Multivariate distributions: scatter/line plot, density plot, grids
Dimensional reduction
Statistical maps
Prerequisites for admission
Basic knowledge of calculus
Teaching methods
The course will combine face-to-face lessons with classroom exercises in small groups under the supervision of the teacher. Part of the course will include practical methods for statistical analysis in python.
Teaching Resources
Von der Linden, Wolfgang, Volker Dose, and Udo Von Toussaint. Bayesian probability theory: applications in the physical sciences. Cambridge University Press, 2014.

Bohm, Gerhard, and Günter Zech. Introduction to statistics and data analysis for physicists. Vol. 1. Hamburg: Desy, 2010.
Assessment methods and Criteria
The examination consists of an oral interview on the topics covered in the course.
FIS/03 - PHYSICS OF MATTER - University credits: 0
FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 0
Lessons: 42 hours
Professor: Zapperi Stefano
Educational website(s)
11-12 Wednesday
zoom (send email for an appointment)