通过几何极值图形模型进行洪水风险估计
Flood risk estimation via geometric extremal graphical models
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中文总结 AI 辅助
研究利用多元几何极值理论新框架，通过定义规范函数，引入简单和复杂模型，应用于河网极端流量分析，模型拟合良好且外推性能强，还引入校正系数，计算同时洪水概率展示了方法的整体效用。
中文摘要 AI 辅助
我们利用多元几何极值理论的新框架对河网中多个位置的河流极端流量进行统计分析。当前几何框架内的方法限于相对较低维度，这对洪水风险估计不足，因河网测量站数量常达10至20多个。为在高维创建简约模型，我们将几何极值图形模型的近期理论工作转化为统计实践。用块图以结构化方式定义几何极值中的关键对象——规范函数，块图是表达河网的自然方式。我们引入简单和复杂模型，应用于英格兰西北部普雷斯顿附近河网10个位置的极端流量，模型拟合良好且外推性能强。还引入几何框架的校正系数以解决边际概率潜在的高估或低估问题。通过计算河网四个位置同时发生洪水的概率说明了我们方法的整体效用。
英文摘要
We exploit the new framework of multivariate geometric extreme value theory for the statistical analysis of river flow extremes at multiple locations on a river network. Current methodologies within the geometric framework are limited to a relatively low number of dimensions. This is insufficient for the purposes of flood risk estimation, since the number of gauging stations on a river network is often of the order $10-20+$. In order to create a parsimonious model in higher dimensions, we translate recent theoretical work on geometric extremal graphical models into statistical practice. We define the gauge function, a key object in geometric extremes, in a structured way using block graphs, which are a natural way of expressing the river network. We introduce both simple models, and more complex ones that can accommodate both simultaneous and non-simultaneous flows, and apply them to extreme flows at 10 locations on a river network around Preston, in north-west England. The models are shown to fit well and indicate strong extrapolation performance. We also introduce a correction coefficient for the geometric framework to address potential over- or under-estimation of marginal probabilities. The overall utility of our approach is illustrated through calculation of probabilities of simultaneous flooding at four locations on the network.
