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.

翻译：极端降水的空间图在防洪中至关重要。为生成降水重现期图，我们提出了一种新方法，用于模拟空间分布的时间序列集合，在该方法中，传统极值理论中典型的渐近假设被放宽。我们引入了一个贝叶斯层次模型，该模型考虑了事件幅度和发生分布中可能存在的潜在变异性，这些变异性通过隐式的时间与空间过程来描述。空间依赖性由地理协变量表征，而未被协变量完全描述的效果则通过层次结构中的空间结构来捕捉。通过模拟研究以及针对美国北卡罗来纳州每日极端降雨的实际应用，展示了该方法的性能。结果表明，与现有先进技术相比，我们显著降低了估计的不确定性。