A strong foundation in probability and statistics (cf. e.g. Jacod and Protter, Probability Essentials, 2004, Chapters 1 to 23) Basic knowledge of the R language

Extreme value theory is based on different principles than those of conventional statistics; it is designed to study and model exceptional events rather than the average characteristics of natural phenomena.

This one-week introductory course will start by presenting exploratory tools to analyze the behavior of extreme values in environmental and insurance data. This will help to motivate the basic principles of the statistical modeling of extreme values and the distributions that characterize them.

The two common approaches for assessing the risk of extreme events at a given level, i.e. the block maxima and the peaks over threshold approach, will be introduced and illustrated with real data examples. The course will then cover the non-stationary, the multivariate and the spatio-temporal extensions of the basic theory.

The R statistical software (freely available at www.r-project.org) will be used in the practicals, as it contains many easily accessible resources for studying and modeling extremes.

The course will be composed of lectures and practical sessions.

Lectures will include :

- Introduction to the extreme value paradigm

- Univariate extreme value theory (probabilistic framework and statistical inference with block maxima and peaks over threshold)

- Multivariate extreme value theory

- Non-stationary extreme value theory

- Spatio-temporal extreme value theory

- Current research trends and perspectives

During the practicals, the students will use dedicated packages in R to apply the concepts learnt during the lectures on real or simulated data.

Continuous evaluation of practical work