Lecturer: Giuseppe De Nicolao  

Course name: Identificazione dei modelli e analisi dei dati (mn)
Course code: 062122
Degree course: Ingegneria per l'Ambiente e il Territorio, Ingegneria Informatica
Disciplinary field of science: ING-INF/04
The course relates to:
University credits: CFU 6
Course website: http://sisdin.unipv.it/

Specific course objectives

Knowledge of basic notions of probability theory (conditional probability, independence, random variable, mean, variance, ...) and statistics (estimators, hypothesis tests, confidence intervals, linear regression, ...). Ability to use software tools for the analysis of experimental data and the identification of simple models (estimation of mean and variance, correlation coefficient, linear regression, ...).

Course programme

Basics of Probability Theory

• notion of probability;
• independence, conditional probability, total probability theorem and Bayes theorem;
• Bernoulli trials, Poisson events;
• definition of Random Variable (R.V.), cumulative ditribution and probability density functions, functions of R.V.;
• mode, mean ad moments of a R.V.;
• multivariate R.V.: probability density function, moments, independence, incorrelation, functions of joint R.V.;
• Law of Large Numbers, Gaussian R.V., Central Limit Theorem.

Basics of Statistics and Data Analysis

• notion of estimator;
• sample moments and their properties;
• confidence intervals for the sample mean, Student's t;
• basics of statistical tests;
• linear in-parameter models: the least squares method;
• Gauss-Markov estimator;
• choice of model complexity: F-test, objective criteria (FPE, AIC, MDL);
• introduction to software tools for model identification and data analysis.

Course entry requirements

Basic notions of set theory, logics, notions of limit, derivative, and integral, maximisation of functions of either one or several variables. Systems of linear equations and matrix calculus.

Course structure and teaching

Lectures (hours/year in lecture theatre): 32
Practical class (hours/year in lecture theatre): 19
Practicals / Workshops (hours/year in lecture theatre): 10
Project work (hours/year in lecture theatre): 0

Suggested reading materials

Marco Bramanti. Teoria della probabilità e statistica. Progetto Leonardo, Bologna.

G. De Nicolao, R. Scattolini. Identificazione Parametrica. Edizioni CUSL, Pavia.

A. Papoulis. Probability, Random Variables, and Stochastic Processes. MCGraw-Hill.

Testing and exams

During and at the end of the course two written tests will be carried out on the first and second part of the lectures, respectively. Passing both tests is equivalent to passing the exam. Otherwise, the student has to pass a written exam covering the entire course program.