Bayesian Variable Selection in Generalized Extreme Value Regression: Modeling Annual Maximum Temperature

Abstract

In many applications, interest focuses on assessing relationships between covariates and the extremes of the distribution of a continuous response. For example, in climate studies, a usual approach to assess climate change has been based on the analysis of annual maximum data. Using the generalized extreme value (GEV) distribution, we can model trends in the annual maximum temperature using the high number of available atmospheric covariates. However, there is typically uncertainty in which of the many candidate covariates should be included. Bayesian methods for variable selection are very useful to identify important covariates. However, such methods are currently very limited for moderately high dimensional variable selection in GEV regression. We propose a Bayesian method for variable selection based on a stochastic search variable selection (SSVS) algorithm proposed for posterior computation. The method is applied to the selection of atmospheric covariates in annual maximum temperature series in three Spanish stations.