Statistics

The course is a foundational activity of the program and it introduces fundamental statistical topics and concepts which are further used and exploited in later courses.
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. The course presents some statistical tools to analyse data, and especially weather/climate data, with a focus on regression approaches which are particularly suited to explore how several variables can affect climate systems.

Students will be able to correctly carry out a statistical analysis of climate-related variables using a statistical software, identifying the most suitable statistical approach for the problem under study and identifying potential benefits and pitfall of various analytical approaches. They will be able to present the results of an statistical analysis, highlighting the most relevant outcomes.
Students will be able to correctly use and interpret the methods presented in the course.

No formal pre-requisite. The course will make use of some mathematics and statistics concepts such as functions, integrals, derivatives, matrices, distributions, estimation and hypothesis testing so students should have the background of an elementary statistics course (at STAT-101 level). It is also expected that students have some notions of how to use a data-analysis language such as R, Python, Matlab or Stata. Students who feel they do not have the necessary familiarity with these topics are highly encouraged to self-study some of these material before the beginning of class and to discuss with the course instructor the best course of action for their learning.

The course presents some introductory and more advanced statistical methods such as:
* data visualisation and exploratory data analysis
* summary statistics
* estimation approaches for distribution fitting: method of moments, maximum likelihood and Bayesian inference
* statistical inference and hypothesis testing
* regression methods (simple and multiple linear regression, generalised linear models)

The practical implementation of the statistical methods presented will be showcased via adequate statistical software (e.g. R)

Students are encouraged to suggest topics relevant to their research program.

Lecture notes and additional external material identified by the instructor. Furthermore, these text might prove a useful reference

Daniel S. Wilks, Statistical Methods in the Atmospheric Sciences, 2005, Academic Press
Michael Trosset, An Introduction to Statistical Inference and Its Applications with R, CRC
Dan E. Kelley. Oceanographic Analysis with R. Springer-Verlag, New York, October 2018.

During the term students will be asked to carry out two assignments in which they will be asked to perform a data-analysis task applying the methods discussed in class. Each assignment is worth 8 points: students who obtain less than 4 points on an assignment will be asked to improve their submission until their submitted work reach a sufficient level (ie it is assessed to be at least 4/8 points).
Students who have reached the minimum required scorse in the data analysis task can take parte in the written exam, which worth 16 points. The written exam will last 45 minutes and will assess the understanding of the more theoretical concepts presented the course.

Theoretical lectures complemented by lab classes. The statistical software used in the course is R (www.r-project.org) and students are encouraged to bring their laptop to class.

English

oral