  Flexible spatial models that allow transitions between tail dependence
classes have recently appeared in the literature. However, inference for these
models is computationally prohibitive, even in moderate dimensions, due to the
necessity of repeatedly evaluating the multivariate Gaussian distribution
function. In this work, we attempt to achieve truly high-dimensional inference
for extremes of spatial processes, while retaining the desirable flexibility in
the tail dependence structure, by modifying an established class of models
based on scale mixtures Gaussian processes. We show that the desired extremal
dependence properties from the original models are preserved under the
modification, and demonstrate that the corresponding Bayesian hierarchical
model does not involve the expensive computation of the multivariate Gaussian
distribution function. We fit our model to exceedances of a high threshold, and
perform coverage analyses and cross-model checks to validate its ability to
capture different types of tail characteristics. We use a standard adaptive
Metropolis algorithm for model fitting, and further accelerate the computation
via parallelization and Rcpp. Lastly, we apply the model to a dataset of a fire
threat index on the Great Plains region of the US, which is vulnerable to
massively destructive wildfires. We find that the joint tail of the fire threat
index exhibits a decaying dependence structure that cannot be captured by
limiting extreme value models.
