Probabilistic Modeling
A.Y. 2019/2020
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.
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.
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.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
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.
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.
Suggested readings Module II:
"Nonparametric estimation", by Fabienne Comte, 2017, Ed. Spartacus-Idh (https://spartacus-idh.com/liseuse/978-2-36693-030-6/)
"Nonparametric Statistical Methods Using R", by John Kloke, Joseph W. McKean, 2014. Chapman and Hall/CRC .
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 (https://spartacus-idh.com/liseuse/978-2-36693-030-6/)
"Nonparametric Statistical Methods Using R", by John Kloke, Joseph W. McKean, 2014. Chapman and Hall/CRC .
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.
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
Professors:
Leorato Samantha, Nicolussi Federica
Shifts:
-
Professors:
Leorato Samantha, Nicolussi FedericaProfessor(s)
Reception:
Next office hours: Thursday 17.04 online only (send an email to request an appointment); Thursday 24.04 from 9:30 to 12:30, online only (send an email to request an appointment); Tuesday 29.04 from 10:30 to 12, Wednesday 30.04 from 14 to 15:30
Room 32 third floor