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.
The course is part of a three-course statistics path which is offered to doctoral students of the Department: the path is composed of a first introductory course (PHD154 Data Analysis with Statistical Programming) which precedes two more advanced non-sequential course (PHD076 Statistical Methods for Climate Change Analysis and PHD124 Applied Time Series). Students who are interested in gaining a more solid background in statistical sciences are highly encouraged to follow all courses and to discuss with the instructor of the course for their PhD program the best course of action.

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 follow the course PHD154 Data Analysis with Statistical Programming which is offered in the Environmental Sciences PhD program 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 some assignments in which they will be asked to perform a data-analysis task using the methods discussed in class. The assignments will be assessed by means of peer-assessment: students will read and critically evaluate their peers data analysis reports.
Students who have completed in a satisfactory manner all assignments are allowed to take a written exam which 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).

English

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