STATISTICAL MODELS: GENERALIZED LINEAR MODELS AND EXTENSIONS

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 adapt to the different background and previous experiences this course is part of a 4-course series which is available to doctoral students of the Department. The courses are

* Introductory Statistics
* Regression models and distribution fitting
* Statistical models: generalised linear models and extensions
* Spatio-temporal statistical models

Each course is worth 3 credits. Students from the Science and Management of Climate Change must take (at least) two courses. Students from the Environmental Sciences program can take as many courses as needed. Students who are interested in gaining a more solid background in statistical sciences are highly encouraged to follow all courses.

It is recommended that all students discuss with the instructors of the courses, 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 prerequisites, although students are assumed to be familiar with basic statistical concepts and linear regression methods, topics covered for example in the Introductory Statistics and Regression models and distribution fitting courses. 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 methods for statistical modeling. In particular, the following topics will be covered:
* the extension of linear models to the case of non-normal data: generalized linear models (e.g., logistic and poisson models)
* the extension of linear models to the case of nonlinear relationships: additive models
* further extensions of linear models

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
Julian Faraway. Linear models with R. CRC Press
Julian Faraway. Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models. CRC Press
Simon Wood, Generalized Additive Models | An Introduction with R (second edition). CRC Press
Andrew Gelman, Jennifer Hill and Aki Vehtari, Regression and Other Stories, Cambridge University 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.

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.

English

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