UCSC-SOE-17-10: A Bayesian Spatial Model for Exceedances Over a Threshold

Fernando Ferraz do Nascimento and Bruno Sansó
06/02/2017 04:23 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 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.