  Uncertainty in return level estimates for rare events, like the intensity of
large rainfall events, makes it difficult to develop strategies to mitigate
related hazards, like flooding. Latent spatial extremes models reduce
uncertainty by exploiting spatial dependence in statistical characteristics of
extreme events to borrow strength across locations. However, these estimates
can have poor properties due to model misspecification: many latent spatial
extremes models do not account for extremal dependence, which is spatial
dependence in the extreme events themselves. We improve estimates from latent
spatial extremes models that make conditional independence assumptions by
proposing a weighted likelihood that uses the extremal coefficient to
incorporate information about extremal dependence during estimation. This
approach differs from, and is simpler than, directly modeling the spatial
extremal dependence; for example, by fitting a max-stable process, which is
challenging to fit to real, large datasets. We adopt a hierarchical Bayesian
framework for inference, use simulation to show the weighted model provides
improved estimates of high quantiles, and apply our model to improve return
level estimates for Colorado rainfall events with 1% annual exceedance
probability.
