Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although the tools for statistical modeling of univariate extremes are well-developed, extending these tools to model spatial extreme data is an active area of research. In this paper, in order to make inference about spatial extreme events, we introduce a new nonparametric model for extremes. We present a Dirichlet-based copula model that is a flexible alternative to parametric copula models such as the normal and t-copula. The proposed modelling approach is fitted using a Bayesian framework that allow us to take into account different sources of uncertainty in the data and models. We apply our methods to annual maximum temperature values in the east-south-central United States.

中文翻译：

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极端非参数空间模型：极端温度数据的应用。

估计极端温度事件的概率很困难，因为跨时间的记录有限，并且需要将这些事件的分布外推到无法观测的位置，而不仅仅是平均值。另一个相关问题是需要表征不同地点极端事件估计概率的不确定性。尽管用于单变量极值统计建模的工具已得到很好的发展，但将这些工具扩展到对空间极值数据进行建模仍是一个活跃的研究领域。在本文中，为了对空间极端事件进行推断，我们引入了一种新的极端非参数模型。我们提出了一个基于 Dirichlet 的 copula 模型，它是参数 copula 模型（例如 normal 和t-系词。建议的建模方法使用贝叶斯框架进行拟合，该框架允许我们考虑数据和模型中的不同不确定性来源。我们将我们的方法应用于美国中东部-中南部的年最高温度值。