  In this work, we develop a constructive modeling framework for extreme
threshold exceedances in repeated observations of spatial fields, based on
general product mixtures of random fields possessing light or heavy-tailed
margins and various spatial dependence characteristics, which are suitably
designed to provide high flexibility in the tail and at sub-asymptotic levels.
Our proposed model is akin to a recently proposed Gamma-Gamma model using a
ratio of processes with Gamma marginal distributions, but it possesses a higher
degree of flexibility in its joint tail structure, capturing strong dependence
more easily. We focus on constructions with the following three product
factors, whose different roles ensure their statistical identifiability: a
heavy-tailed spatially-dependent field, a lighter-tailed spatially-constant
field, and another lighter-tailed spatially-independent field. Thanks to the
model's hierarchical formulation, inference may be conveniently performed based
on Markov chain Monte Carlo methods. We leverage the Metropolis adjusted
Langevin algorithm (MALA) with random block proposals for latent variables, as
well as the stochastic gradient Langevin dynamics (SGLD) algorithm for
hyperparameters, in order to fit our proposed model very efficiently in
relatively high spatio-temporal dimensions, while simultaneously censoring
non-threshold exceedances and performing spatial prediction at multiple sites.
The censoring mechanism is applied to the spatially independent component, such
that only univariate cumulative distribution functions have to be evaluated. We
explore the theoretical properties of the novel model, and illustrate the
proposed methodology by simulation and application to daily precipitation data
from North-Eastern Spain measured at about 100 stations over the period
2011-2020.
