REGRESSION MODELS

Statistics provides a powerful approach to make sense of data and to take into account the uncertainties which come from the randomness of complex systems. To provide PHD students with the most suitable statistical training for their research needs and to accommodate different backgrounds and prior experience, this module is part of a series of two courses, each consisting of two modules. The structure of the courses is designed to fit students with varying levels of familiarity with statistical tools (or econometrics, machine learning, etc.). The courses are structured as follows:

Introduction to Statistics
* Introductory Statistics
* Regression models and distribution fitting

Advanced Statistical Modelling
* Statistical models: generalised linear models and extensions
* Spatio-temporal statistical models

Each course is worth 6 credits. Students in Science and Management of Climate Change must take only one exam (but can take both), while students in Environmental Sciences may take two exams. All students may attend all modules, which is encouraged for those interested in acquiring a stronger background in statistical sciences.

Students are advised to discuss with the course instructors, their PhD supervisor and/or the PhD director the most suitable combination of courses to take for their PhD plan.

Students will be able to correctly carry out a statistical analysis of environmental and climatic variables using statistical software, identifying the most suitable statistical approach for the problem under study and identifying potential benefits and pitfalls of various analytical approaches.

No formal pre-requisite, although the course builds on statistical techniques and methods presented in most bachelor-level statistics course and covered in the Introductory Statistics module (such as descriptive statistics, hypothesis testing). The course will make use of some mathematical and statistical concepts such as functions, integrals, derivatives, matrices, distributions, estimation and hypothesis testing. Students are also expected to have some knowledge of how to use R or other data analysis software (Stata, Python, Matlab).

The course presents basic and advanced statistical methods such as:
* estimation approaches for fitting distributions: method of moments, maximum likelihood and Bayesian inference
* statistical inference and hypothesis testing.
* simple and multiple regression methods.

Practical implementation of the statistical methods discussed in the course will be presented using appropriate statistical software (e.g., R).

Students are encouraged to suggest topics that are of particular interest within their research programs.

Lecture notes, slide and other material provided by the course instructor. The following textbooks can be used as reference material

Daniel S. Wilks, Statistical Methods in the Atmospheric Sciences, 2005, Academic Press
Dan E. Kelley. Oceanographic Analysis with R. Springer-Verlag, New York, October 2018
Julian Faraway. Linear models with R. CRC Press

The examination will take place in the computer lab.
Students will be asked to answer a few written questions and to carry out a data-analysis task, providing a small report on their analysis.
The grade will be based on the number of correct answers provided in the written questions and on the level of the presentation for the data analysis task. In particular, the following items will be evaluated: clarity of the presentation and, appropriateness of the statistical approaches and data visualization methods, readability of the code.

written

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

Votazioni
- 27-30: Correct answers; appropriate use of technical language; excellent presentation of statistical analysis results in terms of analysis accuracy, result visualization/presentation, and code readability.
- 22-26: Generally correct answers, though sometimes expressed with not entirely appropriate and/or proficient use of technical language; satisfactory presentation of statistical analysis results, with largely correct analyses, good result visualization/presentation, and generally readable and executable code.
- 18-21: Only partially correct answers, with inconsistent and sometimes inappropriate use of technical language; fundamentally correct statistical analyses, though presented in a not entirely satisfactory manner, with code that is not always fully readable and/or executable.

Teaching will be organized in:
a) lessons on the main theoretical concepts and the description of the various methods;
b) exercises in which the theoretical concepts are put into practice, writing code, analyzing data, interpreting and communicating the results.