  Spatial maps of extreme precipitation are crucial in flood protection. With
the aim of producing maps of precipitation return levels, we propose a novel
approach to model a collection of spatially distributed time series where the
asymptotic assumption, typical of the traditional extreme value theory, is
relaxed. We introduce a Bayesian hierarchical model that accounts for the
possible underlying variability in the distribution of event magnitudes and
occurrences, which are described through latent temporal and spatial processes.
Spatial dependence is characterized by geographical covariates and effects not
fully described by the covariates are captured by spatial structure in the
hierarchies. The performance of the approach is illustrated through simulation
studies and an application to daily rainfall extremes across North Carolina
(USA). The results show that we significantly reduce the estimation uncertainty
with respect to state of the art techniques.
