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Title: A hierarchical max-infinitely divisible process for extreme areal precipitation over watersheds Authors:  Raphael Huser - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Benjamin Shaby - Penn State University (United States)
Gregory Bopp - Pennsylvania State University (United States)
Abstract: Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit weakening spatial dependence at increasingly extreme levels, limiting max-stable process models for block maxima have a rigid dependence structure that does not capture this type of behavior. In order to model block maxima at sub-asymptotic regimes, we suggest using models from a broader family of max-infinitely divisible (max-id) processes, which retain appealing properties reflecting the specific dependence structure of maxima, while allowing for weakening spatial dependence at increasingly high levels. We will first present general construction principles for max-id processes and discuss how flexible asymptotically independent max-id models may be designed. We will then describe a Bayesian max-id process, whose likelihood function admits a hierarchical representation in terms of random effects, and which scales well to large datasets. The proposed model is constructed using flexible random basis functions that are estimated from the data, allowing for straightforward inspection of the predominant spatial patterns of extremes. We apply our model to extreme precipitation in eastern North America, and show that the proposed model adequately captures the extremal behavior of the data.