Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain

We propose a Bayesian hierarchical model for spatial extremes on a large domain. In the data layer a Gaussian elliptical copula having generalized extreme value (GEV) marginals is applied. Spatial dependence in the GEV parameters are captured with a latent spatial regression with spatially varying coefficients. Using a composite likelihood approach, we are able to efficiently incorporate a large precipitation dataset, which includes stations with missing data. The model is demonstrated by application to fall precipitation extremes at approximately 2600 stations covering the western United States, -125E to -100E longitude and 30N to 50N latitude. The hierarchical model provides GEV parameters on a $1/8$th degree grid and consequently maps of return levels and associated uncertainty. The model results indicate that return levels vary coherently both spatially and across seasons, providing information about the space-time variations of risk of extreme precipitation in the western US, helpful for infrastructure planning.