COMPUTATIONAL STATISTICS AND SIMULATION

This course belongs to the educational activities of the Master in Computer Science that allow the student to acquire advanced instruments for data analysis. The objective of the course is to provide an introduction to R for the application of statistical computational and simulation methods.

Regular and active participation in the teaching activities offered by the course will enable students to:

1. Knowledge and understanding:
1.1 To know the nonparametric approach to statistical inference.
1.2 To know the basic concepts for designing composite indicators.
1.3 To know copulas to simulate high dimensional distributions with complex dependence structures.
1.4 To know the basic concepts of statistical quality controls of products and services.

2. Ability to apply knowledge and understanding:
2.1 To know how to apply nonparametric statistical methods.
2.2 To know how to define and apply composite indicators.
2.3 To know how to apply copulas to simulate multivariate distributions.
2.4 To know how to design and apply quality control charts.
2.5. To know how to apply autonomously the basic computational and programming tools of the R environment.

3. Ability to judge:
3.1 To be able to select the most suitable nonparametric statistical methods for the problem at hand.
3.2 To be able to design the most suitable composite indicator for the problem at hand.
3.3 To be able to select and parametrize the most suitable copula to simulate the multivariate distribution of interest.
3.4 To be able to design the most suitable quality control chart for the problem at hand.

4. Communication skills:
4.1 To be able to communicate the results to the various stakeholders.
4.2 To be able to interact with the lecturer and the other students during the theoretical lessons and practical applications.

5. Learning skills:
5.1 To be able to take lecture notes to integrate and clarify the content of the referral teaching material.
5.2 To be able to self evaluate by addressing the lecturer’s questions and solving exercises.

Basic knowledge of descriptive statistics, probability, parametric inference, coding.

0) Introduction
Computational statistics. Statistical simulation. Statistical hypothesis testing. Parametric and nonparametric tests.

1) Comparing central tendency
The bi- and tri-aspect tests

2) Comparing variability
The Ansari-Bradley test, the permutation Pan test, the permutation O'Brien test.

3) Jointly comparing central tendency and variability
The Lepage test, the Cucconi test, the multisample Cucconi test

4) Comparing distributions
The Kolmogorov-Smirnov test, the Cramer-Von Mises test

5) Testing for correlation and concordance
The Spearman test, the Kendall test, the Kendall-Babington Smith test, a permutation test for concordance.

6) Analysis of high-throughput data: genomics, metabolomics.

7) How to simulate multivariate distributions with complex dependence structures using Elliptical and Archimedean copulas.

8) Bootstrap: variance estimation, tests, confidence intervals.

9) Design and uncertainty analysis of composite indicators.

10) Statistical quality control in the Industry 4.0 era. Shewhart, CUSUM, EWMA charts for product and services. LCL, UCL, ARL computation.

Open source books on R
Scientific papers
Lecture notes

The achievement of the course objectives is assessed through a written exam. The exam includes both open questions and exercises related to computational statistics, including nonparametric statistical methods, statistical simulation, uncertainty analysis of composite indicators, quality control charts. Key-points to pass the exam are: to be able to select the most suitable method for the problem at hand, to apply it correctly and interpret the results. At the end of the course at least a simulated exam will be performed.

a) theoretical lessons describing the various concepts and methods
b) practicals with data analyses and result discussion and communication.

English

None.

written