Statistical Methods and Applications

MARIA BRIGIDA FERRARO
MARIA BRIGIDA FERRARO

Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses. Students will be able
- to understand the theoretical foundations of the most important methods;
- to appropriately implement and apply computational statistical procedures;
- to interpret the results deriving from their applications to real data.

Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.

Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.

Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.

Communication skills
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test. Communication skills will be also developed through group activities.

Learning skills
Students who pass the exam have learned computational techniques useful in the statistical analysis and to work self-sufficiently to face with the complexity of the statistical problems.

Learning goals
The main goal of the course is to learn about common general computational tools and methodologies to perform reliable statistical analyses.

Students will be able
to understand the theoretical foundations of the most important methods;
to appropriately implement and apply computational statistical procedures;
to interpret the results deriving from their applications to real data. .

(a) Knowledge and understanding
After attending the course, students will know and understand the most important computational techniques in statistical analysis. In addition, students will be able to appropriately implement the learned tools with the statistical software R and to develop original ideas often in a research context.
(b) Applying knowledge and understanding
At the end of the course, students will be able to formalize statistical problems from a computational point of view, to apply the learned methods to solve them, also in contexts not covered in the lessons, and to interpret the results deriving from their applications to real data.
c) Making judgements
Students will develop critical skills through the application of computational methodologies to a wide range of statistical problems and through the comparison of alternative solutions to the same problem by using different tools. Furthermore, they will learn to interpret critically the results obtained by applying procedures to real datasets.
(d) Communication skills.
By studying and carrying out practical exercises, students will acquire the technical-scientific language of the discipline, which must be suitably used in the final written test. Communication skills will also be developed through group activities.
(e) Learning skills
Students who pass the exam have learned computational techniques useful in statistical analysis and to work self-sufficiently to face the complexity of the statistical problems.

B.Sc courses on linear algebra, probability calculus, statistical inference, multivariate analysis, basic programming skills.

Introduction to computational statistics and R programming (2 hours)
Methods for Generating Random Variables (6 hours)
Visualization of Multivariate Data (2 hours)
Monte Carlo Integration and Variance Reduction (8 hours)
Monte Carlo methods in Inference (6 hours)
Bootstrap and Jackknife (12 hours)
Permutation Tests (6 hours)
Optimization and solving nonlinear equations (6 hours)
EM optimization methods (2 hours)
Fuzzy clustering algorithms (10 hours) [only for 9 ECTS course]
Group projects (12 hours) [only for 9 ECTS course]

- M. L. Rizzo (2008): Statistical Computing with R. Chapman & Hall, Boca Raton.
- G. H. Givens, J. A. Hoeting (2005): Computational Statistics. Wiley & Sons, Hoboken.

- B. Efron, B.J. Tibshirani (1993): An Introduction to the Bootstrap. Chapman and Hall/CRC.

- Lectures
- Tutorial sessions in computer laboratory

Course attendance is strongly recommended. In case of impossibility to attend the lessons, it is suggested to contact the teacher.

- The learning assessment consists of a written exam in computer laboratory lasting 2 hours. The final written text contains both theoretical and practical questions aimed at analyzing real data with R (2/3 - 6 cfu)

- Group project (1/3 - 3 cfu)

1) Example of theoretical question:
What is the difference between the Newton's method and the Secant one?

2) Example of R question:
The parameter of interest (theta) is the expected value of the variable X.
Obtain a NORMAL, a BASIC and a PERCENTILE bootstrap confidence interval # estimate f or theta (confidence level = 95%).
[Use the function boot.ci ONLY to check the results of your implementation]