A Hierarchical Max-infinitely Divisible Process for Extreme Areal Precipitation Over Watersheds
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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. We propose a flexible Bayesian model from a broader family of max-infinitely divisible processes that allows for weakening spatial dependence at increasingly extreme levels, and due to a hierarchical representation of the likelihood in terms of random effects, our inference approach scales 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. In addition, the described process possesses max-stability as a special case, making inference on the tail dependence class possible. 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.
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