Data spaces/Modelli statistici is an integrated course aimed at presenting advanced methods of Statistics and the mathematical foundations of Machine Learning within a unifying view. The part of the course called Data Spaces is borrowed by the course with the same name offered in Software Engineering, see the relative webpage. The present webpage i smade of a general part related to the integrated course and a specific part (below) describing the Modelli Statistici part, the more statistical section of the course.

The contents of the course are based on the 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 specialised 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.

A good knowledge of Mathematical Analysis and Linear Algebra as presented in the first two bachelor years of any Engineering School and a basic education in elementary Probability and Mathematical Statistics worth around 12 credits.

(Data Spaces specific part, borrowed from the course called Data Spaces) Generalities on data representation (topologies, metrics, dissimilarities). Classification: logistic regression, LDA, QDA, tree-based methods, SVM. Resampling methods. Unsupervised statistical Learning: PCA, ICA, MDS. Time series and some spatial statistics (with elements of kriging). (Modelli statistici specific part) Linear models (regression, ANOVA) with quantitative and qualitative predictors, transformations, model choice. Simultanous inference in linear models (multiple comparison, ranking and testing, Tukey, Scheffé) . Generalized linear models (e.g. logistic, Poisson and Cox regression). Linear and nonlinear mixed effect models. Bayesian Statistics and Bayesian Networks.

Traditional lectures will alternate with computer sessions, either in lab or in class. The student will bring his/her own computer and install the necessary software in order to be able to follow the development of the course.

Slides for most of the classes will be made available on the course webpage. In addition, the student is recommended to consult the following references. - 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.

Modalitą 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 disabilitą 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'Unitą Special Needs, al fine di permettere al/la docente la declinazione pił idonea in riferimento alla specifica tipologia di esame.