Spatial models for the distribution of extremes

Statistical models for the occurrence of extreme or rare events has been applied in a variety of areas, but little work has been done in extending these ideas to spatial data sets. Here, a brief introduction to the theory of extreme-value statistics is given, and a hierarchical Bayesian framework is used to incorporate a spatial component into the model. Two examples are used to motivate the applications of statistics for extremes: high values of ozone pollution and high rates of daily rainfall. In the case of the ozone example, a spatial-temporal model is compared to the extreme-value model, and results for these two very different approaches are remarkably similar. Finally, this tutorial chapter highlights a number of areas of extreme-value statistics that require more research, such as algorithms to compute (or sample) posteriors from a Bayesian analysis.