Probabilistic modeling

A.A. 2019/2020
Insegnamento per
6
Crediti massimi
40
Ore totali
SSD
SECS-S/01
Lingua
Inglese
Obiettivi formativi
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, to perform an empirical analysis and to report and discuss its results.

Struttura insegnamento e programma

Edizione attiva
Responsabile
SECS-S/01 - STATISTICA - CFU: 6
Lezioni: 40 ore
STUDENTI FREQUENTANTI
Programma
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; Density estimation; nonparametric regression.
Propedeuticità
There are no specific prerequisites, but students must be familiar with Statistics and Probability from at least a 3-year bachelor course.
In particular: classification of characters and graphic representations; location and scale indices; elements of probability; random variables (see Bernoulli, Binomial and Normal); sample distributions (see sample media, see sample proportion, see sample variance) ­ estimation theory.
Prerequisiti e modalità di esame
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.). 
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.
Metodi didattici
Each topic will be presented during the classical lectures and the use of specific R packages will be illustrated in the lab lectures.
Materiale didattico e bibliografia
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 .

Slides, Exercises, Lab tutorial with R will be available on the web page
STUDENTI NON FREQUENTANTI
Programma
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; Density estimation; nonparametric regression.
Prerequisiti e modalità di esame
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.). 
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.
Materiale didattico e bibliografia
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 .

Slides, Exercises, Lab tutorial with R will be available on the web page
Periodo
Secondo trimestre
Periodo
Secondo trimestre
Modalità di valutazione
Esame
Giudizio di valutazione
voto verbalizzato in trentesimi
Docente/i
Ricevimento:
martedì 10:30-13:30.
stanza 32 DEMM
Ricevimento:
Il ricevimento subirà le seguenti variazioni settimana 1/07 al 7/07: RICEVIMENTO SOSPESO settimana 8/07 al 14/07: RICEVIMENTO fissato il giorno lunedì 8/07 h 9:30-12:30 settimana 15/07 al 21/07: RICEVIMENTO fissato il giorno giovedì 18/07 h 9:30-12:30
DEMM, stanza 29, 3° p