  Extreme environmental phenomena such as major precipitation events manifestly
exhibit spatial dependence. Max-stable processes are a class of
asymptotically-justified models that are capable of representing spatial
dependence among extreme values. While these models satisfy modeling
requirements, they are limited in their utility because their corresponding
joint likelihoods are unknown for more than a trivial number of spatial
locations, preventing, in particular, Bayesian analyses. In this paper, we
propose a new random effects model to account for spatial dependence. We show
that our specification of the random effect distribution leads to a max-stable
process that has the popular Gaussian extreme value process (GEVP) as a
limiting case. The proposed model is used to analyze the yearly maximum
precipitation from a regional climate model.
