We develop a method for probabilistic prediction of extreme value hot-spots in a spatio-temporal framework, tailored to big datasets containing important gaps. In this setting, direct calculation of summaries from data, such as the minimum over a space-time domain, is not possible. To obtain predictive distributions for such cluster summaries, we propose a two-step approach. We first model marginal distributions with a focus on accurate modeling of the right tail and then, after transforming the data to a standard Gaussian scale, we estimate a Gaussian space-time dependence model defined locally in the time domain for the space-time subregions where we want to predict. In the first step, we detrend the mean and standard deviation of the data and fit a spatially resolved generalized Pareto distribution to apply a correction of the upper tail. To ensure spatial smoothness of the estimated trends, we either pool data using nearest-neighbor techniques, or apply generalized additive regression modeling. To cope with high space-time resolution of data, the local Gaussian models use a Markov representation of the Matérn correlation function based on the stochastic partial differential equations (SPDE) approach. In the second step, they are fitted in a Bayesian framework through the integrated nested Laplace approximation implemented in R-INLA. Finally, posterior samples are generated to provide statistical inferences through Monte-Carlo estimation. Motivated by the 2019 Extreme Value Analysis data challenge, we illustrate our approach to predict the distribution of local space-time minima in anomalies of Red Sea surface temperatures, using a gridded dataset (11315 days, 16703 pixels) with artificially generated gaps. In particular, we show the improved performance of our two-step approach over a purely Gaussian model without tail transformations.

我们针对时空框架开发了一种概率预测极值热点的方法，该方法针对包含重要缺口的大型数据集而量身定制。在这种设置下，无法直接根据数据计算汇总，例如时空范围内的最小值。为了获得此类聚类汇总的预测分布，我们提出了一种两步法。我们首先对边缘分布进行建模，重点是对右尾巴进行精确建模，然后将数据转换为标准的高斯尺度后，我们估计时空局部区域在时域中局部定义的高斯时空依赖模型，其中我们要预测。在第一步中，我们使数据的均值和标准差下降趋势，并拟合空间分解的广义Pareto分布以应用上尾部的校正。为了确保估计趋势的空间平滑性，我们要么使用最近邻技术合并数据，要么应用广义加性回归建模。为了应对高时空分辨率的数据，局部高斯模型使用了基于随机偏微分方程（SPDE）方法的Matérn相关函数的Markov表示。第二步，通过集成的嵌套Laplace近似将它们拟合在贝叶斯框架中。局部高斯模型使用基于随机偏微分方程（SPDE）方法的Matérn相关函数的Markov表示。第二步，通过集成的嵌套Laplace近似将它们拟合在贝叶斯框架中。局部高斯模型使用基于随机偏微分方程（SPDE）方法的Matérn相关函数的Markov表示。第二步，通过集成的嵌套Laplace近似将它们拟合在贝叶斯框架中。R- INLA。最后，生成后验样本以通过蒙特卡洛估计提供统计推断。受2019年极值分析数据挑战的激励，我们使用人工生成的间隙的网格化数据集（11315天，16703像素）说明了我们的方法来预测红海表面温度异常中局部时空最小值的分布。尤其是，我们展示了两步方法相对于没有尾部变换的纯高斯模型的改进性能。