Period and duration
May 2018 – 7.30 hours
Aula Buzano of DISMA, corso Duca degli Abruzzi, third floor
Link to the map
|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|
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:
- methods for statistical learning and their relationship with optimization;
- hierarchical models and Bayesian statistics;
- dependence among random variables and copula theory;
- 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.
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.
- 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.