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Methodology for High-Dimensional Multivariate Extremes

高维多元极值方法

基本信息

批准号：
EP/P002838/1
负责人：
Jennifer Wadsworth
金额：
$ 30.5万
依托单位：
Lancaster University
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2016
资助国家：
英国
起止时间：
2016 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FP002838%2F1
关键词：
Methodology Dimensional Multivariate Extremes

项目摘要

Most people accept that there are risks in our day-to-day lives. However, we also expect that these risks are managed so that the probability of catastrophe is acceptably low, without infringing on our ability to get on with daily life. For example, we could perhaps eliminate flooding by building very high flood defences on all riverbanks, but we choose not to because this would be disproportionate to the risk: diverting money from other necessary services, and creating other inconveniences.In order to manage the risk proportionately, we need to be well informed about the probability of such rare but disastrous events. The question is how can we do this when we may never have witnessed an event of the size we with to protect against? Extreme value theory is the probabilistic theory of rare events, and provides a rational framework for drawing inference about the likelihood of future extremes given data on past extremes. Models for extremes of a single variable (e.g. river flow at a particular gauging station) are relatively well developed. However, most catastrophic events occur when extremes of different variables combine, or aggregate over space. In order to fully understand the risks we therefore need multivariate and spatial models, and in order that these models produce reliable estimates, they should be motivated by extreme value theory. The multivariate and spatial extreme value models that are commonly used today suffer from restrictive assumptions and / or can only be applied to very low dimensions (e.g. to the joint extremes of two variables). The goal of this project is to build new models for multivariate and spatial extremes that are appropriate under more general assumptions, and to extremes of a greater number of variables, so that they are more applicable to the problems of interest. This will enable better estimation of the probability of extreme events, and thus improve our management of these risks.

大多数人都认为我们的日常生活中存在风险。然而，我们也期望这些风险得到管理，使灾难的可能性降低到可接受的程度，而不影响我们继续日常生活的能力。例如，我们也许可以通过在所有河岸上建造非常高的防洪设施来消除洪水，但我们选择不这样做，因为这与风险不成比例：从其他必要的服务中转移资金，并造成其他不便。为了合理地管理风险，我们需要充分了解这种罕见但灾难性事件的概率。问题是，当我们可能从未目睹过我们要防范的规模如此之大的事件时，我们如何做到这一点？极值理论是罕见事件的概率理论，并提供了一个合理的框架，以推断未来极端事件的可能性。单一变量的极值模型（例如，特定测量站的河流流量）相对较完善。然而，大多数灾难性事件发生时，极端的不同变量联合收割机，或聚集在空间。因此，为了充分理解风险，我们需要多变量和空间模型，为了使这些模型产生可靠的估计，它们应该受到极值理论的激励。目前常用的多变量和空间极值模型受到限制性假设的影响，并且/或者只能应用于非常低的维度（例如，两个变量的联合极值）。该项目的目标是建立新的模型，适用于更一般的假设下的多变量和空间的极端情况，以及更多变量的极端情况，使它们更适用于感兴趣的问题。这将有助于更好地估计极端事件的概率，从而改善我们对这些风险的管理。