Modeling risk in complex systems

人类经济日益数字化、城市化和互联互通，随之而来的是越来越容易受到自然和人为灾难的影响。因此，风险管理和备灾对社会和可持续发展至关重要。作为我之前NSERC Discovery Grant的延续，拟议研究计划的长期愿景是为风险管理提供易于处理和灵活的模型。我的长期目标是开发统计模型和推理技术，以揭示大量风险因素中的复杂依赖模式，并量化极端情况下的因果影响。要量化复杂和可能极端的风险，需要超越植根于常态、相关性和回归的传统方法。第一个短期目标是推进我正在进行的关于Copula模型的工作，该模型可以捕获传统发行版无法充分解释的关系。使用基于排名的技术，我将开发混合数据的Copula模型的方法，并设计高维任意分布的独立性测试。我最近关于经验多线性Copula过程的结果也将被用来验证广义线性模型。我的进一步目标是通过学习算法和函数式数据分析技术在大量变量集合中发现依赖模式。第二个短期目标将侧重于极端情况的统计分析。我将研究相依风险的极限行为，并对相依风险的最大值进行推断，例如共同投资组合中可能因共同外部因素而相依的保险索赔。在标准极值理论不适用的中等区域，我将进一步研究Maxima的灵活的max-id模型。机器学习将用于研究洪水或热浪等极端现象背景下出现的0-1模式。为了帮助理解自然灾害的原因并改进其预测，第三个短期目标是研究高分位数的分位数处理效果和极端情况的结构学习算法。拟议的研究计划将显著影响研究人员评估复杂系统风险的方式。将开发的多变量数据和罕见事件的方法将允许捕获比传统统计模型所考虑的更加多样的依赖模式和数据结构。这项研究将在极值分析、相关性建模和因果推理方面取得进展，这些都是广大统计受众感兴趣的。建议的方法将进一步改进保险、风险管理和自然灾害预测方面的做法。结果将通过加拿大和国外的期刊文章和讲座广泛传播；将通过统计计算R项目向最终用户提供软件。

The increasing digitalization, urbanization, and interconnectedness of human economies come with growing vulnerability to natural and man-made catastrophes. Risk management and disaster preparedness are thus of paramount importance for society and sustainable development. In continuation of my previous NSERC Discovery Grant, the long-term vision of the proposed research program is to provide tractable and flexible models for risk management. My long-term goals are to develop statistical models and inference techniques to unravel complex dependence patterns in large collections of risk factors and to quantify causal effects on, and of, extremes. The quantification of complex and possibly extreme risks requires techniques beyond traditional approaches rooted in normality, correlation, and regression. The first short term objective is to advance my ongoing work on copula models, which can capture relationships that can't be adequately accounted for by traditional distributions. Using rank-based techniques, I will develop methodology for copula models for mixed data and devise tests of independence for arbitrary distributions in high dimensions. My recent results on the empirical multilinear copula process will also be used to validate generalized linear models. I further aim to find dependence patterns in large collection of variables through learning algorithms and functional data analysis techniques. The second short term goal will focus on statistical analysis of extremes. I will investigate the limiting behavior of, and develop inference for, maxima of dependent risks such as insurance claims in a common portfolio which may be dependent due to common external factors. I will further study flexible max-id models for maxima in the medium regime for which the standard extreme-value theory does not apply. Machine learning will be used to study 0-1 patterns that arise in the context of extreme phenomena, such as floods or heatwaves. To help understand the causes of natural hazards and improve their forecasts, the third short-term goal is to study quantile treatment effects for high quantiles and structure learning algorithms for extremes. The proposed research program will significantly impact the way researchers assess risk in complex systems. The methodology for multivariate data and rare events that will be developed will allow to capture much more versatile dependence patterns and data structures than those accounted for by traditional statistical models. The research will make advances in extreme-value analysis, dependence modeling, and causal inference which are of interest to a wide statistical audience. The proposed methods will further lead to improved practices in insurance, risk management, and natural hazard forecasting. The results will be disseminated broadly through journal articles and talks in Canada and abroad; software will be made available to end-users through the R Project for Statistical Computing.