Program
Previsional program here
Courses
Extreme Value Theory I
Extreme events are generally related to severely damaging hazards and their inherent scarcity make any decision related to them difficult. The main issue consists in extrapolating from observed levels tounobserved ones and extreme value theory (EVT) provides a class of models to enable such extrapolation. This part of this course is devoted to univariate EVT. Two approaches will be presented : block- maxima and threshold exceedances. Applications will be adressed using the R software.
Extreme Value Theory II
This course represents the next step of the study of univariate extremes (Extremes I) and is devoted to multivariate extreme value theory. Two approaches will be also presented : block-maxima and threshold exceedances. An introduction to spatial extreme modelling will be proposed. Finally applications on real data set will be adressed with the R software.
Geostatistics
For spatially recorded data, taking into account the resulting spatial dependency is a crucial issue for inference. Assuming an underlying random field with stationary increments, modelling the spatial dependency amounts to estimate a variogram, that will be the main tool for predicting/simulating spatial or spatiotemporal processes. Various kriging techniques for spatial prediction will be presented and some applications in environmental field will be adressed with R software.
Epidemiology
In the last decades, the study of incidence/mortality data in a region has been established as a basic tool in public health data analysis. This permits to identify potential risk factors of a certain disease and to discover health inequalities. This course will cover classical techniques for risks estimation, simple statistical models for smoothing risks and more sophisticated statistical models including spatial dependence. Real data will be used to illustrate the procedures.
Spatial on lattice
In epidemiology, data are often collected on a discrete set of sites, for instance administrative districts. Markov Random Fields are useful for modelling such data. The spatial dependence is expressed locally, the distribution at one site depending on its neighbours. We focus on Besag's auto-models, a class of Markov Random Fields. We present various models and their inference, with examples in the epidemiological context and their extension to spatio- temporal modelling.
Food risk
Certain foods may contain varying amounts of chemicals which may cause major health problems when accumulating inside the body in excessive doses. These events are most of the time rare. In a static approach, extreme value theory can be used to model the tail of the exposure distribution but it does not account for the kinetics of the chemical of interest in the human body. Ruin models can be adapted to model the dynamic of the exposure.
Research presentation