  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.
