Advanced Multivariate Statistics

A.Y. 2019/2020
Lesson for
6
Max ECTS
40
Overall hours
SSD
SECS-S/01
Language
English
Learning objectives
The course will be divided in two parts, Multivariate statistics and Computational Statistics.

The first part takes up the concepts of multivariate statistical analysis, regression and classification techniques, multidimensional scaling, but introduces a robust approach. Furthermore, Bayesian networks will be presented. During the course applications to real situations in presence of outliers and mixed type data will be presented, the statistical packages as FSDA toolbox for MATLAB and R libraries will be used.

The second part will focus on advanced computational statistics for simulation-based analysis and introduce students to basic concepts, techniques and applications of computational statistics to be used in finance and economics. Students will be also introduced to a basic knowledge of statistical software and programming (R, Python and OpenBUGS) for Monte Carlo simulation in order to solve practical problems.

Students will achieve skills for doing independent study and research.

Course structure and Syllabus

Active edition
Yes
Responsible
SECS-S/01 - STATISTICS - University credits: 6
Lessons: 40 hours
ATTENDING STUDENTS
Syllabus
Fist Part
(i) Introduction of Robust Statistics
(ii) Robust regression (S, MM, LMS)
(iii) Introduction to FSDA toolbox for MATLAB
(iv) Forward Search Methods (FS)
(v) Robust Multivariate analysis
(vi) Analysis of Mixed type data
(vii) Bayesian Networks
Second Part
(i) Computer-intensive resampling methods: the Bootstrap and the Jackknife.
(ii) Pseudo-random numbers generators: linear congruential generators; multiply-with-carry generators; lagged-Fibonacci generators; the Mersenne twister generator.
(iii) Random variable generators: the inverse transform method; the accept-reject method; the Box-Muller method; mixture representation.
(iv) Monte Carlo numerical methods and estimation algorithms: the Newton-Raphson algorithm, Monte Carlo integration, the EM algorithm, importance sampling.
(v) Monte Carlo Markov Chain methods: the Metropolis-Hastings algorithm; The Gibbs sampler.
(vi) Software for MCMC and hierarchical Bayesian analysis: the OpenBUGS software
NON-ATTENDING STUDENTS
Syllabus
Fist Part
(i) Introduction of Robust Statistics
(ii) Robust regression (S, MM, LMS)
(iii) Introduction to FSDA toolbox for MATLAB
(iv) Forward Search Methods (FS)
(v) Robust Multivariate analysis
(vi) Analysis of Mixed type data
(vii) Bayesian Networks
Second Part
(i) Computer-intensive resampling methods: the Bootstrap and the Jackknife.
(ii) Pseudo-random numbers generators: linear congruential generators; multiply-with-carry generators; lagged-Fibonacci generators; the Mersenne twister generator.
(iii) Random variable generators: the inverse transform method; the accept-reject method; the Box-Muller method; mixture representation.
(iv) Monte Carlo numerical methods and estimation algorithms: the Newton-Raphson algorithm, Monte Carlo integration, the EM algorithm, importance sampling.
(v) Monte Carlo Markov Chain methods: the Metropolis-Hastings algorithm; The Gibbs sampler.
(vi) Software for MCMC and hierarchical Bayesian analysis: the OpenBUGS software
Lesson period
First trimester
Lesson period
First trimester
Assessment methods
Esame
Assessment result
voto verbalizzato in trentesimi
Professor(s)
Reception:
Wed 4.30PM-7.30PM. Next office hours: Sept 18th, 2019, 4.30PM
Room 37, 3rd Floor.