CAREER: Hierarchical Models for Spatial Extremes

罕见事件可能会对经济、基础设施以及人类健康和福祉产生严重影响。但为了做出合理的决策，了解最严重的事件可能会有多大是至关重要的。PI将专注于开发统计工具，以了解最极端事件的空间结构。这些新工具将改进现有的模型，因为它们将更现实，更易于计算。PI还将应用这些工具来帮助科学家和政策制定者研究内陆洪水、野火和沿海风暴潮等严重环境现象带来的风险。此外，PI将组织讲习班，促进统计学和地球科学研究的更紧密结合，并开发研究生课程和一本侧重于地球科学现代统计方法的教科书。PI将开发空间极端事件的随机模型，这些模型1)足够灵活，可以跨越不同类别的极端依赖，2)允许通过可以为大数据集计算的似然函数进行推理。它通过有条件地表示随机依赖关系来实现这些建模目标，这将导致期望的尾部依赖性质，并允许通过马尔可夫链蒙特卡罗(MCMC)进行有效的推理。第一个研究部分将使用极大-无穷可分(极大-id)过程开发空间极值的次渐近模型，极大-无限可分(极大-id)过程是基于条件表示的极限最大稳定过程类的推广。第二个研究部分将开发基于空间高斯过程的尺度混合的极值的亚渐近空间模型。PI将对拟议的分层指定的max-id和Scale混合过程所引起的联合尾部依赖进行紧密交织的计算开发和理论解释。最后，PI将把这些模型应用于具有高社会影响的问题，如极端降水风险、野火易感性和沿海风暴潮暴露。PI将加强极值统计学家与气候和大气科学家、减缓研究人员和利益攸关方之间的联系，途径是1)一年两次的天气和气候极端国际讲习班，2)空间统计学博士水平课程，其中将包括空间极端情况的新进展和应用，以及3)为地球科学家编写教科书《现代统计学》。PI还将在宾夕法尼亚州立大学的可持续气候风险管理(SCRIM)暑期学校增加极端问题模块，并为SIRM的电子资源和互动教材做出贡献，供教育工作者、决策者、未被充分代表的群体和普通公众使用。PI将加强与负责沟通和减轻极端环境现象对公众构成的风险的政府机构的现有合作。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Rare events can have crippling effects on economies, infrastructure, and human health and well being. But in order to make sound decisions, understanding how large the most severe events are likely to be is imperative. The PI will focus on developing statistical tools for understanding the spatial structure of the most extreme events. These new tools will improve on existing models because they will be both more realistic and more computationally tractable. The PI will also apply these tools to help scientists and policymakers study risks posed by severe environmental phenomena like inland floods, wildfires, and coastal storm surges. Furthermore, the PI will organize workshops to foster closer integration of statistical and Earth science research, as well as develop graduate courses and a textbook focused on modern statistical methods for Earth science.The PI will develop stochastic models for extreme events in space that are 1) flexible enough to transition across different classes of extremal dependence, and 2) permit inference through likelihood functions that can be computed for large datasets. It will accomplish these modeling goals by representing stochastic dependence relationships conditionally, which will induce desirable tail dependence properties and allow efficient inference through Markov chain Monte Carlo (MCMC). The first research component will develop sub-asymptotic models for spatial extremes using max-infinitely divisible (max-id) processes, a generalization of the limiting max-stable class of processes, based on a conditional representation. The second research component will develop sub-asymptotic spatial models for extremes based on scale mixtures of spatial Gaussian processes. The PI will conduct closely interwoven computational development and theoretical explication of the joint tail dependence that the proposed hierarchically specified max-id and scale mixture processes induce. Finally, the PI will apply these models to problems of high societal impact, such as extreme precipitation risk, wildfire susceptibility, and coastal storm surge exposure. The PI will enhance connections between extreme value statisticians and communities of climate and atmospheric scientists, mitigation researchers, and stakeholders, through 1) biannual international workshops on weather and climate extremes, 2) a Ph.D. level course in spatial statistics which will include new advances and applications of spatial extremes, and 3) writing the textbook Modern Statistics for Earth Scientists. The PI also will add modules on extremes to Penn State's Sustainable Climate Risk Management (SCRiM) summer school, and contribute to SCRiM's electronic resources and interactive teaching materials for educators, decision makers, underrepresented groups, and the general public. The PI will strengthen existing collaborations with government agencies which are responsible for communicating and mitigating risk to the public posed by extremal environment phenomena.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.