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Spatial maps of extreme precipitation are crucial in flood protection. Withthe aim of producing maps of precipitation return levels, we propose a novelapproach to model a collection of spatially distributed time series where theasymptotic assumption, typical of the traditional extreme value theory, isrelaxed. We introduce a Bayesian hierarchical model that accounts for thepossible underlying variability in the distribution of event magnitudes andoccurrences, which are described through latent temporal and spatial processes.Spatial dependence is characterized by geographical covariates and effects notfully described by the covariates are captured by spatial structure in thehierarchies. The performance of the approach is illustrated through simulationstudies and an application to daily rainfall extremes across North Carolina(USA). The results show that we significantly reduce the estimation uncertaintywith respect to state of the art techniques.

A hierarchical Bayesian non-asymptotic extreme value model for spatial data