Probabilistic Modeling

A.Y. 2019/2020
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 and nonparametric statistical methods.
In particular, in the nonparametric modelling module, students will learn the most important statistical tools that can be used in situations where a lack of information on the data generating process may advise to perform inference under vague assumptions.
In the graphical modelling module, students will gain knowledge of techniques that help to describe and easily represent the dependence relationships among a set of variables, 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 and nonparametric modelling 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 methods from one of the modules at their choice, proving their comprehension of the topics and their ability to apply them and to discuss and report the results. A grasp of the content of both the modules is expected, and will be verified through a brief oral examination on the module excluded from the empirical exercise.
Course syllabus and organization

Unique edition

Lesson period
Second trimester
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.
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.
Suggested readings Module II:
"Nonparametric estimation", by Fabienne Comte, 2017, Ed. Spartacus-Idh (
"Nonparametric Statistical Methods Using R", by John Kloke, Joseph W. McKean, 2014. Chapman and Hall/CRC .
Assessement 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
Educational website(s)
Wednesday 13:30 -16:30. Until the continuation of the COVID-19 emergency measures, the office hours will be arranged via conference call. Students who need an appointment are invited to contact me by email to arrange an e-meeting
Room 32 DEMM
Wednesday 10:00-12:00 and 13:30-14:30 (from Wednesday 7/01/2020)
DEMM, office 29, 3th floor