LEARNING OUTCOMES

The course aims to provide a precise overview of statistical inference at an intermediate level. The first part concerns classical mathematical statistics, based on likelihood, with some hints on simulation-based techniques. The second part of the course focuses on the main regression and classification techniques. In particular, generalized linear models for both discrete and continuous responses will be treated. Some non-parametric regression and classification methods will then be illustrated. Finally, classical methods of validation, model selection, and dimensionality reduction will be addressed.

AIMS AND LEARNING OUTCOMES

The course is divided into two parts:

                1) Some topics in classical inferential Statistics: the main families of univariate and multivariate distributions, simulation, theory of statistical models, the likelihood and its properties.

                2) Statistical models for classification and regression. Multiple regression, generalized linear model theory, logistic regression and regression for count data, nonparametric techniques. Nonparametric techniques. Model selection techniques.

All the topics will be accompanied by practical exercises in R, so that the student can also combine the understanding of the theory with the ability to apply correct statistical analyses in real contexts and to read correctly the output of the statistical procedures.

Knowledge and understanding: Students will know the main techniques and the main tools for inferential statistics. They must be able to frame these tools in general terms (both theoretical and applied), and to analyze the underlying mathematical and statistical background.

Ability to apply knowledge and understanding: Students will be able to identify, when faced with problems from different contexts, the correct analysis. Moreover, they will be able to evaluate the results obtained through statistical software.

Making judgments: Students will have to become aware of the potential and limits of the statistical techniques, through the analysis of examples and case studies.

Communication skills: Students must be able to use the correct technical statistical language for the communication of the results and for the description of the techniques.

Learning skills: Students will develop adequate learning skills in order to continue with further studies about other aspects of the subject and different fields of application than those illustrated. Furthermore, they must also be able to use the R software in a general context.

PREREQUISITES

The classical content of the introductory courses in Mathematical and Statistics for Economics and Business.

TEACHING METHODS

Lectures and computer lab tutorials with R. Discussion of case studies.

SYLLABUS/CONTENT

0. Introduction and basic recalls on estimation and hypothesis testing.

1. Some families of discrete and continuous probability distributions.

2. Multivariate distributions.

3. Simulation. Distribution-based simulation and agent-based simulation.

4. Likelihood and sufficiency. Maximum likelihood estimation. Information. The exponential family.

5. Multiple linear regression and k-NN techniques.

6. Generalized linear models theory.

7. Logistic regression and regression for count data.

8. Model selection and regularization.

RECOMMENDED READING/BIBLIOGRAPHY

Evans, Rosenthal, Probability and Statistics. The Science of Uncertainty, Second edition.

James G, Witten D, Hastie T and Tibshirani R, An Introduction to Statistical Learning. With Applications in R. Springer (available from the Authors’ webpage).

Further readings will be taken from:

Casella G and Berger RL, Statistical Inference. Duxbury

Efron B and Hastie T, Computer Age Statistical Inference. Algorithms, Evidence, and Data Science. Stanford University (available from the Authors’ webpage).

Additional course materials (both in Italian and in English) will be available on AulaWeb.