PhD Course: Introductory lectures to Bayesian Networks

Professors
Brandimarte, Fontana, Gasparini, Pellerey

Period and duration
May 2018 – 7.30 hours

Location
Aula Buzano of DISMA, corso Duca degli Abruzzi, third floor
Link to the map

Detailed schedule

Description

Knowledge of the basics of probability theory and inferential statistics is a prerequisite.
The course aims at completing the education of Ph.D. students about:

1. methods for statistical learning and their relationship with optimization;
2. hierarchical models and Bayesian statistics;
3. dependence among random variables and copula theory;
4. statistical methods for the Design of Experiments (DOE).

All methods will be illustrated in practice using the R or the SAS software on applications to industrial, scientific
and management problems, in order to make the course useful and appealing to a broad audience of Ph.D.
students.
Program

Statistical learning, multivariate analysis and optimization:

• The origins: least squares and max likelihood
• Optimization in standard multivariate methods (PCA, clustering)
• Optimization modeling approaches in fitting and estimation
• The bias-variance tradeoff: regularization and robust optimization, and applications to regression and classifiers (support vector machines)
• Statistics and stochastic optimization: approximate dynamic programming

Hierarchical Bayesian Models:

• the Bayesian approach to statistical inference;
• conjugate priors and analytical solutions in closed form;
• industrial and scientific applications;
• hierarchical models;
• numerical computations by Markov Chain Monte Carlo methods.

Copula theory:

• analysis of dependence properties of random vectors by means of copulas;
• basic properties and main families of copulas;
• frailty models and inference methods for the frailty parameters;
• concordance and indexes of concordance.

Design of Experiments:

• orthogonal fractional factorial designs;
• saturated designs;
• optimal designs.

Official course webpage on Polito.it