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Bayesian Inference for Peaks Over Threshold Models for Multivariate and Spatial Extremes

多元和空间极值的阈值模型峰值的贝叶斯推理

基本信息

批准号：
1513076
负责人：
Bruno Sanso
金额：
$ 30.93万
依托单位：
University of California-Santa Cruz
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-07-15 至 2019-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1513076&HistoricalAwards=false
关键词：
Bayesian Inference Peaks Over Threshold

项目摘要

Extreme value theory is a branch of probability and statistics that focuses on the study of rare events. There are many areas of science and technology where such methods find applications. Examples include the quantification of actuarial risk, estimation of large fluctuations in financial markets, and the estimation of maximum water flow. Of particular relevance for our society is the study of extreme climate events. Historical records of climate related variables provide evidence that there is an intensification of extreme weather. Climate projections indicate that the frequency and intensity of events with catastrophic potential will increase even further. This research focuses on the development of statistical methods that will enable careful assessment of the uncertainties related to extreme events. The proposed methods will focus on models that look jointly at several variables and apply to observations collected in large spatial domains. Probabilistic assessment of the uncertainties in the occurrence of rare events will be made possible by a Bayesian approach. This will provide a powerful tool for rational decision and policy making.In this project, novel methodology for the statistical analysis of the distributions of extreme values is proposed. The methods are based on using the amounts in excess of a fixed threshold for the variables of interest, or peaks over thresholds (POT). POT methods to perform Bayesian inference for (a) multivariate observations, (b) spatially indexed fields, and (c) fields of multivariate observations in space will be developed and implemented. In extreme value theory, the focus is on extrapolation as scarce extreme observations are used to describe the behavior of the tails of the distribution. The theory and the methods for inference on univariate extreme values are firmly established and fully developed. For multivariate problems, it is key to model the joint tail dependence of the different variables. In this sense, the theory is well understood, but inferential methods are not as straightforward as in the univariate case. This is especially true for POT methods. A further level of complication is introduced when dealing with georeferenced data. In fact, in the spatial setting, it is impossible to write the full likelihood of realistic POT models for observations collected at an arbitrary number of locations. This research focuses on the development of methods that (a) are conceptually clear to specify using a simple factorization that is at the core of Bayesian hierarchical models, (b) allow for fully integrated Bayesian inference that accounts for all estimation uncertainty and quantifies it probabilistically, (c) have theoretically sound asymptotic properties, (d) provide flexible characterizations of a wide range of tail dependence, and (e) are computationally feasible for large spatial domains.

极值理论是概率论和统计学的一个分支，主要研究罕见事件。这种方法在许多科学和技术领域都有应用。例如，精算风险的量化、金融市场大幅波动的估计以及最大水流量的估计。与我们社会特别相关的是对极端气候事件的研究。气候相关变量的历史记录提供了极端天气加剧的证据。气候预测表明，具有灾难性潜力的事件的频率和强度将进一步增加。这项研究的重点是制定统计方法，以便能够仔细评估与极端事件有关的不确定性。所提出的方法将侧重于共同研究几个变量的模型，并适用于在大空间域中收集的观测数据。将通过贝叶斯方法对罕见事件发生的不确定性进行概率评估。本计画提出一种新的极值分布统计分析方法。该方法基于使用超过感兴趣的变量的固定阈值的量，或超过阈值的峰值（POT）。 POT方法进行贝叶斯推断（a）多元观测，（B）空间索引字段，（c）领域的多元观测空间将开发和实施。在极值理论中，重点是外推，因为很少的极端观测值被用来描述分布尾部的行为。一元极值推理的理论和方法得到了牢固的建立和充分的发展。对于多变量问题，关键是对不同变量的联合尾部依赖进行建模。在这个意义上，理论是很好理解的，但推理方法不像在单变量的情况下那么简单。这对于POT方法来说尤其如此。在处理地理参考数据时，会出现更复杂的情况。事实上，在空间环境中，不可能为在任意数量的位置收集的观测值编写真实POT模型的全部可能性。这项研究的重点是开发的方法，（a）是概念上明确指定使用一个简单的因子分解，这是在贝叶斯分层模型的核心，（B）允许完全集成的贝叶斯推理，占所有估计的不确定性和量化它的概率，（c）有理论上健全的渐近性质，（d）提供灵活的表征范围广泛的尾部依赖，和（e）对于大的空间域在计算上是可行的。