|SCIENTIFIC DISCIPLINARY SECTOR||SECS-S/01|
Prerequisites (for future units)
The course aims at providing a thorough account of classical and modern statistical inference at an intermediate level, focusing both on the classical likelihood method and on simulation techniques. Then, the theory and applications of regression and classification models will be introduced, with special attention to socio-economic applications.
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.
The course is divided into two parts:
1) Some topics in classical inferential Statistics: the main families of univariate and multivariate distributions, the likelihood and its properties, simulation and the bootstrap.
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.
The typical skills of the introductory courses in Mathematics and Statistics for Economics and Business.
Lectures and computer lab tutorials with R. Discussion of case studies.
0. Introduction and basic recalls on estimation and hypothesis testing.
1. Some families of discrete and continuous probability distributions.
2. Multivariate distributions.
3. Likelihood and sufficiency. Maximum likelihood estimation. Information. The exponential family.
4. Simulation and the bootstrap.
5. Multiple linear regression and k-NN techniques.
6. Theory of Generalized linear models.
7. Logistic regression and regression for count data.
8. Model selection and regularization.
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 will be available on AulaWeb.
This class follows the Department calendar for the 2nd semester.
All class schedules are posted on the EasyAcademy portal.
The exam is a written exam which consists of three parts:
1) a general essay question
2) one or more questions on specific topics
3) a comment on a R output.
The complete exam rules will be available on the class Aulaweb page. For attending students, intermediate exams will be organized. Such intermediate exam will contribute to the final mark.
If there will be the need of on-line exams, due to the Covid-19 outbreak, we try to keep the exam in written form with upload of the answer sheets.
As far as possible, the questions of the written exam 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.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.