A Bayesian Spatial Model for Exceedances Over a Threshold

Extreme value theory focuses on the study of rare events and uses asymptotic properties to estimate their associated probabilities. Easy availability of georeferenced data has prompted a growing interest in the analysis of spatial extremes. Most of the work so far has focused on models that can handle block maxima, with few examples of spatial models for exceedances over a threshold. Using a hierarchical representation, we propose a spatial process, that is obtained by perturbing a Pareto process. Our approach uses conditional independence at each location, within a hierarchical model for the spatial field of exceedances. The model has the ability to capture both, asymptotic dependence and independence. We use a Bayesian approach for inference of the process parameters that can be efficiently applied to a large number of spatial locations. We assess the flexibility of the model and the accuracy of the inference by considering some simulated examples. We illustrate the model with an analysis of data for temperature and rainfall in California.