The generalized extreme value (GEV) distribution is a popular model for analyzing and forecasting extreme weather data. To increase prediction accuracy, spatial information is often pooled via a latent Gaussian process on the GEV parameters. Inference for such hierarchical GEV models is typically carried out using Markov chain Monte Carlo (MCMC) methods. However, MCMC can be prohibitively slow and computationally intensive when the number of latent variables is moderate to large. In this paper, we develop a fast Bayesian inference method for spatial GEV models based on the Laplace approximation. Through simulation studies, we compare the speed and accuracy of our method to both MCMC and a more sophisticated but less flexible Bayesian approximation. A case study in forecasting extreme wind speeds is presented.

翻译：普遍极端值分布是分析和预测极端天气数据的流行模式。为了提高预测的准确性,空间信息往往通过GEV参数的潜伏高斯进程汇集在一起。对这种等级的GEV模型的推论通常使用Markov连锁 Monte Carlo(MCMC)方法进行。然而,当潜伏变量的数量从中到大时,MCMC可能极其缓慢,而且计算密集。在本文中,我们为基于拉普尔近似的空间GEV模型开发了一种快速贝叶斯推论方法。通过模拟研究,我们将我们的方法速度和准确性与MMC和一种更复杂但不那么灵活的Bayesian近似方法进行比较。我们介绍了预测极端风速的案例研究。