OVERVIEW

The course aims at providing a thorough account of classical and modern statistical inference at an intermediate level. The topics range from classical inference based on likelihood to regression and classification techniques, with special attention to applications to Economics and Social Sciences.

AIMS AND CONTENT

LEARNING OUTCOMES

The purpose of the course on “Statistical models” is to present some fundamental techniques in Statistics (likelihood-based estimation, regression and classification methods, Markov processes) so that the student is able to understand such techniques both theoretically and in practice, and to analyze the use of these techniques in several fields of application.

AIMS AND LEARNING OUTCOMES

The course is divided into three 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, logistic and Poisson regression, nonparametric techniques. Nonlinear regression.

                3) Discrete Markovian models. Markov chains and applications.

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 an introductory course in Statistics.

TEACHING METHODS

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

SYLLABUS/CONTENT

1. Introduction to statistical models.

2. Some families of discrete probability distributions.

3. Some families of continuous probability distrubutions. Normality tests.

4. Multivariate distributions. Conditional distributions and conditional expectation.

5. Simulation. Mixture distributions and density estimation.

6. Likelihood and sufficiency. Maximum likelihood estimation. Information.

7. The exponential family.

8. Recalls on the multiple linear regression.

9. Generalized linear models. Logistic and Poisson regression. Linear discriminant analysis.

10. Linear model selection and regularization.

11. Regression splines.

12. Markov chains. Transition probabilities. Recurrence and transience.

13. Stationary distribution and convergence.

14. First passage times and simulations.

RECOMMENDED READING/BIBLIOGRAPHY

Textbooks:

Mood AM, Graybill FA and Boes DC, Introduction to the theory of statistics, 3rd edition (available on Aulaweb).

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

Further readings:

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 on the authors' webpage).

Italian version of the first book: Mood AM, Graybill FA and Boes DC, Introduzione alla statistica, Mc-Graw Hill.

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

TEACHERS AND EXAM BOARD

Exam Board

FABIO RAPALLO (President)

CORRADO LAGAZIO

LUCA PERSICO

LESSONS

LESSONS START

2nd Semester

Class schedule

STATISTICAL MODELS

EXAMS

EXAM DESCRIPTION

Due to the COVID outbreak, if the on-site exams will be allowed, the exam will be a Written exam. There will be three intermediate exams – only for student who attend the lectures on a regular basis – which replace the final exam.  The complete exam rules are available on the Aulaweb page of the course.

If we need to turn to on-line exams, the exam will be a written exam with upload of the exam manuscript. The complete exam rules are available on the Aulaweb page of the course, where students will find all updated information.

ASSESSMENT METHODS

The written exam consists of three parts:

1) a general essay question

2) one or more questions on specific topics

3) a comment on a R output.

As far as possible, the questions are chosen in order to cover all the topics of the course. The general question aims at assessing the degree of knowledge of the subject and the acquisition of the correct technical language, the specific questions are aimed at assessing the critical ability of the student, while the purpose of the comment to the output is to evaluate the application capabilities.

Exam schedule