Data spaces/Modelli statistici is an integrated course aimed at presenting advanced methods of Statistics and the mathematical foundations of Machine Learning with a unifying view.

The contents of the course are based on the statistical frequentist and Bayesian concepts for data analysis and interpretation, with the addition of a few new ideas coming from Machine Learning. The student will learn the mathematical and logical foundations of data analysis and will be educated to the critical use of specialized software. Through the analysis of a variety of case study, the student is expected to be able to perform the analysis of new data in several different application areas.

The students are supposed to know calculus and the basics of probability and statistics (equivalent to around 15 credit background). Frequentist theory of estimation and testing will be assumed. Bayesian ideas will be introduced in the course.

Linear models (regression, ANOVA) with quantitative and qualitative predictors, transformations, model choice. Gaussian responses and what to do when they are not. Generalized linear models: responses other than gaussian (e.g. logistic, Poisson and Cox regression). Linear and nonlinear mixed effect models. Bayesian Statistics. Bayesian Networks.

Traditional lectures will alternate with computer sessions, either in lab or in class.

- The BUGS Book: A Practical Introduction to Bayesian Analysis by David Lunn, Chris Jackson, Nicky Best, Andrew Thomas, David Spiegelhalter. CRC Press 2013. - Bayesian Networks with examples in R. by Marco Scutari and Jean-Baptiste Denis CRC Press 2015. - Foundations of linear and generalized linear models by Alan Agresti. Wiley, 2015. - Statistical analysis of designed experiments by Ajit C. Tamhane. Wiley 2009. - R in action by R.I. Kabacoff. Manning 2011.

Modalità di esame: Prova orale obbligatoria;

Exam: Compulsory oral exam;

... At the end of the course, a list of case studies seen in the course will be provided, together with explanations, references and software. During the oral exam each student will be assigned at random two case studies from the list, which he/she will have to discuss thoroughly. The student will comment on the specific aspects of the case study, on its methodological foundations and on the software used. The student will have to be able to connect the specific details of the case studies to general principles and methodologies.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.