KOCH Erwan

Natural disasters may have considerable impact on society as well as on the (re-)insurance industry. Max-stable processes are ideally suited for the modelling of the spatial extent of such extreme events, but it is often assumed that there is no temporal dependence. Only a few papers have introduced spatiotemporal max-stable models, extending the Smith, Schlather and Brown‒Resnick spatial processes. These models suffer from two major drawbacks: time plays a similar role to space and the temporal dynamics are not explicit. In order to overcome these defects, we introduce spatiotemporal max-stable models where we partly decouple the influence of time and space in their spectral representations. We introduce both continuous- and discrete-time versions. We then consider particular Markovian cases with a max-autoregressive representation and discuss their properties. Finally, we briefly propose an inference methodology which is tested through a simulation study.

Accurate stochastic simulations of hourly precipitation are needed for impact studies at local spatial scales. Statistically, hourly precipitation data represent a difficult challenge. They are non-negative, skewed, heavy tailed, contain a lot of zeros (dry hours) and they have complex temporal structures (e.g., long persistence of dry episodes). Inspired by frailty-contagion approaches used in finance and insurance, we propose a multi-site precipitation simulator that, given appropriate regional atmospheric variables, can simultaneously handle dry events and heavy rainfall periods. One advantage of our model is its conceptual simplicity in its dynamical structure. In particular, the temporal variability is represented by a common factor based on a few classical atmospheric covariates like temperatures, pressures and others. Our inference approach is tested on simulated data and applied on measurements made in the northern part of French Brittany.Comment: Presented by Erwan Koch at the conferences: - 12th IMSC, Jeju (Korea), June 2013 - ISI WSC 2013, Hong Kong, Aug.2013. Invited speaker in the session "Probabilistic and statistical contributions in climate research.

This thesis aims at developing tools and models adapted to the study of certain spatial and networked risks. It is divided into five chapters. The first one consists in a general introduction, containing the state of the art within which the various works are included, as well as the main results obtained. Chapter 2 proposes a new multi-site precipitation generator. It is important to have models capable of producing statistically realistic precipitation series. While the models previously introduced in the literature are mainly concerned with daily precipitation, we develop an hourly model. It involves only one equation and thus introduces a dependence between occurrence and intensity, processes often considered as independent in the literature. It includes a common factor taking into account the large-scale atmospheric conditions and a multivariate autoregressive spillover term, representing the local rainfall propagation. In spite of its relative simplicity, this model reproduces very well the intensities, the durations of drought as well as the spatial dependence in the case of Northern Brittany. In Chapter 3, we propose a method for estimating max-stable processes, based on simulated likelihood techniques. Max-stable processes are very well suited to the statistical modelling of spatial extremes, but their estimation is delicate. Indeed, the multivariate density does not have an explicit form and standard estimation methods related to the likelihood cannot be applied. Under appropriate assumptions, our estimator is efficient when the number of temporal observations and the number of simulations tend to infinity. This simulation approach can be used for many classes of max-stable processes and can provide better results than current methods using composite likelihood, especially in the case where only a few time observations are available and the spatial dependence is important.