UCSC-SOE-15-11: A Bayesian Hierarchical Generalized Pareto Spatial Model for Exceedances Over a Threshold

Fernando Ferraz do Nascimento and Bruno Sanso
05/28/2015 03:37 PM
Applied Mathematics & Statistics
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 has generalized Pareto distributions
as its marginals. The process is in the domain of attraction of the
max-stable family. It 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.