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

DATE TIME LOCATION
Thursday, May 10, 2018 From 10:00 to 12:30 Aula Buzano @ DISMA
Thursday, May 17, 2018 From 10:00 to 12:30 Aula Buzano @ DISMA
Thursday, May 24, 2018 From 10:00 to 12:30 Aula Buzano @ DISMA

 

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

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