Abstract
A Bayesian hierarchical framework with a Gaussian copula and a generalized extreme value (GEV) marginal distribution is proposed for the description of spatial dependencies in data. This spatial copula model was applied to extreme summer temperatures over the Extremadura Region, in the southwest of Spain, during the period 1980–2015, and compared with the spatial noncopula model. The Bayesian hierarchical model was implemented with a Monte Carlo Markov Chain (MCMC) method that allows the distribution of the model’s parameters to be estimated. The results show the GEV distribution’s shape parameter to take constant negative values, the location parameter to be altitude dependent, and the scale parameter values to be concentrated around the same value throughout the region. Further, the spatial copula model chosen presents lower deviance information criterion (DIC) values when spatial distributions are assumed for the GEV distribution’s location and scale parameters than when the scale parameter is taken to be constant over the region.
Highlights
Extreme events tend to occur naturally as topics of importance in several sciences—climatology, hydrology, engineering, etc.—and in finance and in the insurance industry
Extreme Value Theory (EVT) is a widely used statistical tool with which to address their study. It is used in several particular scientific fields to model and predict extreme events of precipitation [1,2,3,4,5], temperature [6,7,8], solar climatology [9,10], and financial crises [11,12]
Several theories are used to address the problem of spatial extremes, some examples are max-stable processes [15], Bayesian hierarchical models [16,17,18], and copula theory [19,20,21,22]
Summary
Extreme events tend to occur naturally as topics of importance in several sciences. —climatology, hydrology, engineering, etc.—and in finance (financial crisis studies) and in the insurance industry. In the first layer, it is assumed that the data follow a distribution with unknown parameters, while in a second layer, the variability of these parameters is modeled spatially by regression techniques This kind of model has been used in many extreme rainfall studies [28,29,30,31] and in temperature studies [32,33]. There must be an increase in uncertainty in the information transferred to the ungauged site when the correlation between observatories is taken into account This key point of considering the spatial dependence among the data can be accomplished by means of a copula model.
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