基于多元极值的几何表示的风险集概率的贝叶斯模型平均
Bayesian model averaging of risk set probabilities using a geometric representation of multivariate extremes
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中文总结 AI 辅助
本研究针对多元极值建模，提出结合删失似然的贝叶斯模型平均方法，在小样本下提升尾风险概率预测性能，并通过火灾气象指数验证其环境应用价值。
中文摘要 AI 辅助
利用几何视角对多元极值进行建模，可借助多元点云的形状对联合尾概率进行推断。尽管原始的几何极值统计框架是完全参数化的，依赖于为给定密度唯一定义形状的 gauge 函数，但更新的方法引入了半参数和非参数替代方案以提升灵活性。我们提出一种建模方法，保留参数框架的简洁性，同时通过贝叶斯模型平均（BMA）增加灵活性，以改进尾风险概率的预测。与使用截断径向似然的先前工作不同，我们提出使用删失似然，发现其在预测均方误差方面始终表现更好，尤其在小样本场景中，不过代价是偏差增大。为生成预测，我们采用简单的重要性采样方案，其精度似乎与更定制化的方法相当。最后，我们将该方法应用于两个火灾气象指数，这些指数旨在捕捉火灾风险的部分正交方面，以说明该方法在环境应用中的实用性。
英文摘要
Modeling multivariate extremes using a geometric perspective leverages the shape of the multivariate point cloud to make inference on joint tail probabilities. While the original statistical framework for geometric extremes was fully parametric, relying on a gauge function that uniquely defines the shape for a given density, newer methods have introduced semi- and non-parametric alternatives to increase flexibility. We propose a modeling approach that retains the simplicity of the parametric framework but adds flexibility by using Bayesian model averaging (BMA) to improve prediction of tail risk probabilities. In contrast to previous works that use a truncated radial likelihood, we propose using a censored likelihood, which we find has consistently better performance in terms of predictive mean squared error, particularly in small-sample settings, although at the expense of increased bias. To generate predictions, we use a simple importance sampling scheme that seems to match the accuracy of more bespoke methods. Finally, we apply our approach to two fire weather indices, which are designed to capture somewhat orthogonal aspects of fire risk, to illustrate our method's practical utility in environmental applications.
