composite likelihood function) to properly account for using a pairwise likelihood when computing standard errors \[@godambe-1987a\]. Recently, @genton-2011 extend this approach using composite likelihood based on trivariate densities. The problem of spatial prediction, conditional on observations, for max-stable random fields (analogous to Kriging for Gaussian processes) has also proven difficult. The recent conditional sampling algorithm of @wang-2010a is capable of producing both predictions and prediction standard errors for most spatial max-stable models of practical interest, subject to discretization errors that can be made arbitrarily small.

Bayesian estimation and inference for max-stable process models for spatial data on a continuous domain has been elusive. Implementing these models in a fully-Bayesian framework has several advantages, including incorporation of prior information and natural uncertainty assessment for model parameters and predictions. Approximate Bayesian methods based on asymptotic properties of the pairwise likelihood function are possible. @ribatet-2010a use an estimated sandwich matrix to adjust the Metropolis ratio within an MCMC sampler, while @shaby-2010c rotates and scales the MCMC sample post-hoc and @smith-2009a use pairwise likelihoods without adjustment. Bayesian models that are not based on max stable processes have been used for analysis of extreme values with spatial structure. @cooley-2007a uses a hierarchical model with a 