  A successful model for high-dimensional spatial extremes should, in
principle, be able to describe both weakening extremal dependence at increasing
levels and changes in the type of extremal dependence class as a function of
the distance between locations. Furthermore, the model should allow for
computationally tractable inference using inference methods that efficiently
extract information from data and that are robust to model misspecification. In
this paper, we demonstrate how to fulfil all these requirements by developing a
comprehensive methodological workflow for efficient Bayesian modelling of
high-dimensional spatial extremes using the spatial conditional extremes model
while performing fast inference with R-INLA. We then propose a post hoc
adjustment method that results in more robust inference by properly accounting
for possible model misspecification. The developed methodology is applied for
modelling extreme hourly precipitation from high-resolution radar data in
Norway. Inference is computationally efficient, and the resulting model fit
successfully captures the main trends in the extremal dependence structure of
the data. Robustifying the model fit by adjusting for possible misspecification
further improves model performance.
