Advanced Multivariate Statistics

A.Y. 2019/2020
Overall hours
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, but introduces a robust approach. Furthermore, Bayesian networks will be presented. During the course applications to real situations 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.
Expected learning outcomes
Students will achieve skills for doing independent study and research, alsoin presence of outliers and deviation form the classical hypothesis. Moreover they will learn computational ans symulation techniques. At the end they will also able to use a variety of different software for advance statistical analsysis.
Course syllabus and organization

Single session

Lesson period
First trimester
Course syllabus
First 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
Prerequisites for admission
No mandatory prerequisites are required, but a good knowledge of statistics and probability fundamentals is strictly reccomended. Matrix algebra and calculus will be beneficial but are not strictly required. Basic programming skills are also useful.
Teaching methods
50 per cent lecture-style classes;
50 per cent classroom interactive teaching activities focused on examples, case studies, research papers and applications in MATLAB, R, Python and OpenBUGS.
Teaching Resources
Suggested reading for insights into some topics in main textbooks:
(i) Introducing Monte Carlo Statistical Methods with R (2010) by C.P. Robert, G. Casella, Springer.
(ii) The BUGS book (2010) by Lunn et al., Taylor & Francis
(iii) Exploring multivariate data with the forward search (2013) by Atkinson, Riani and Cerioli, Springer
(iv) Robust diagnostic regression analysis (2012) by Atkinson and Riani, Springer
(v) Bayesian networks: with examples in R (2014) by Scutari and Denis, Chapman and Hall

Further reading will be suggested during the course.
Other material:
Slides presented in class, Sceintific Papers, Maltab scripts, R scripts, Python notebooks, OpenBUGS files
Assessment methods and Criteria
Some assignments will be delivered and evalueated during the course and a written final project is required. Evaluation of the project will be performed through an oral presentation and examination, in which students will be asked questions about the methods used in the project, the code produced and on the rest of the syllabus.
SECS-S/01 - STATISTICS - University credits: 6
Lessons: 40 hours
Wednesday 2.30PM-5.30PM (appointment suggested, via Teams).
Room 37, 3rd Floor (due to sanitary emergency office hours in person are suspended - Office hours will be held via Teams)
Starting from 20 September 2021 the student reception will be in attendance on Tuesdays from 10.30 to 12 and on Fridays from 10.30 to 12.00. If necessary, it is possible to make an appointment, at the same times, for a remote meeting via Teams.
DEMM, room 30, 3° floor