Introduction; Graphical models for categorical variables; Gaussian Graphical models; Bayesian network; Mixed interaction models; High dimensional Modelling
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.).
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 .
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.