Probabilistic Modeling

A.Y. 2020/2021
Overall hours
Learning objectives
The course of probabilistic modelling aims at enriching the student's choice of methodological tools for data analysis with advanced topics that are not covered by other courses, namely graphical models. In particular, in the graphical modelling module, students will gain knowledge of techniques that provide an elegant framework to compactly represent complex real-wold phenomena, also when the number of variables involved is high.
Expected learning outcomes
Students of this course will acquire a thorough understanding of the theory behind graphical models and the ability to apply these tools to real datasets, through the introduction to specific packages of the R software. In particular, they are required to perform an empirical analysis, using one method from the ones discussed in the class at their choice, proving their comprehension of the topics and their ability to apply them and to discuss and report the results.
Course syllabus and organization

Single session

Lesson period
Second trimester
Lectures will be given through the Microsoft Teams platform according to the official lecture scheduling (synchronous attendance). Moreover, lectures are recorded and made available via streaming on the Microsoft Teams platform (asynchronous attendance). The main topics and the references will be unchanged
Course syllabus
Module I:
Introduction; Graphical models for categorical variables; Gaussian Graphical models; Bayesian network; Mixed interaction models; High dimensional Modelling

Module II
Empirical distribution function and rank based statistics (distribution-free tests); Density estimation; nonparametric regression; other extensions.
Prerequisites for admission
Students are assumed to be acquainted with the basic principles of Probability and Statistics theory (random variables and their characteristics, estimators and their properties (bias, variance, consistency, asymptotic distribution, etc.), law of large numbers and central limit theorem, maximum likelihood methods, etc.). 
Teaching methods
The teaching method is traditional face to face learning. In each module, part of the classes will be held in a laboratory or computer assisted.
Teaching Resources
Suggested readings Module I:
Højsgaard, Søren, David Edwards, and Steffen Lauritzen. Graphical models with R. Springer Science & Business Media, 2012.
Whittaker, Joe. Graphical models in applied multivariate statistics. Wiley Publishing, 2009.
Assessment methods and Criteria
The exam will consist on the preparation and discussion of a written report, on one of the modules of the exam, chosen by the student.
A small oral examination regarding the other part will complete the assessment.
The report has to be prepared in the form of a small paper, where the methods learnt in the exam are applied to real data. The topic of the report will be defined by the students, subject to Professor's approval.
SECS-S/01 - STATISTICS - University credits: 6
Lessons: 40 hours
Professor: Nicolussi Federica
by appointment