Contributions to Spatial Statistics : Species Distributions and Rare Events

This thesis proposes some contributions to the spatial modelling of species distributions and extreme values. Predictive models are increasingly used to model the distribution of species and to estimate the potential effects of global change on biodiversity. Although species distribution models are now widely used, the effects of several factors on their prediction accuracy are mostly unknown. We introduce a method to measure the relative impact of factors on the accuracy of species distribution models. Our approach allows us to identify factors that require more control in the construction of predictive models. The ideas are illustrated by application to plant species in the Swiss Alps. The modelling of spatial extremes, or rare events, is central for the assessment of risks associated to disastrous environmental events. Methods for modelling extremes of time series are well-established, but efficient methods for spatial modelling are still in full development. We investigate the use of asymptotic dependence and independence models based on max-stable processes and their differences in practice. We show how these different models can be used to model threshold exceedances, and we introduce a more efficient approach based on Pareto processes. Finally, we construct a flexible Bayesian hierarchical model for spatial extremes. Our methods are illustrated by applications to rainfall in Switzerland and low temperatures in Finland.