发表机构
University of Göttingen; University of Edinburgh（哥廷根大学; 爱丁堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出尾部光晕概念，定义协变量空间中与极端事件相关的区域，并开发贝叶斯结构化加性分布回归框架进行推断，应用于爱丁堡空气污染数据识别高污染配置。
AI 中文摘要
极端事件通常通过描述协变量如何修改尾部参数的回归模型来研究。然而，在许多应用中，兴趣直接在于识别与尾部事件及超过概率升高相关的协变量空间部分。我们通过尾部光晕（tail halos）——与极端相关的协变量定义区域——来形式化这些思想。风险光晕（risk halos），当存在时，是解释规定比例的超额概率的最小质量协变量区域，而有利光晕（favorable halos）收集条件超过概率超过其边际水平的协变量值。为了使这些集合值对象在低维之外可解释，我们引入了光晕诱导的协变量分布（halo-induced covariate laws），并且当密度存在时，引入相应的光晕密度（halo densities）。我们开发了一个基于扩展广义帕累托边缘分布、协变量相关的copula和spike-and-slab效应选择的贝叶斯结构化加性分布回归框架，以学习边际和联合的光晕诱导协变量分布，同时传播后验不确定性。该方法将用于条件尾部建模的贝叶斯收缩方法扩展到多元体部-尾部建模、非线性效应选择和协变量区域推断。模拟表明，随着样本量的增长，能够恢复相关的非线性效应，并越来越准确地表示有限样本光晕。对爱丁堡PM2.5和NO2极端值的应用揭示了与高污染相关的不同环境和时间配置。
英文摘要
Extreme events are often studied through regression models describing how covariates modify tail parameters. In many applications, however, interest lies directly in identifying the parts of the covariate space associated with tail events and with elevated exceedance probabilities. We formalize these ideas through tail halos, covariate-defined regions associated with extremes. Risk halos, when they exist, are minimum-mass covariate regions accounting for a prescribed fraction of exceedance probability, while favorable halos collect covariate values where conditional exceedance probability exceeds its marginal level. To make these set-valued objects interpretable beyond low dimensions, we introduce halo-induced covariate laws and, when densities exist, corresponding halo densities. We develop a Bayesian structured additive distributional regression framework based on extended generalized Pareto marginals, covariate-dependent copulas, and spike-and-slab effect selection to learn marginal and joint halo-induced covariate laws while propagating posterior uncertainty. The approach extends Bayesian shrinkage methods for conditional tail modeling to multivariate bulk-and-tail modeling, nonlinear effect selection, and covariate-region inference. Simulations show recovery of relevant nonlinear effects and increasingly accurate finite-sample halo representations as sample size grows. An application to PM2.5 and NO2 extremes in Edinburgh reveals distinct environmental and temporal configurations associated with high pollution.
