When investigating extremes of weather variables, it is seldom that a single weather station determines the damage, and extremes may be caused from the combined behaviour of several weather stations. To investigate joint dependence of extreme wind speed, a bivariate generalised extreme value distribution (BGEVD) was considered from frequentist and Bayesian approaches to analyse the extremes of component-wise monthly maximum wind speed at selected weather stations in South Africa. In the frequentist approach, the parameters of extreme value distributions (EVDs) were estimated with maximum likelihood, whereas in the Bayesian approach the Markov Chain Monte Carlo (MCMC) technique was used with the Metropolis–Hastings algorithm. The results showed that when fitted to component-wise maxima of extreme weather variables, the BGEVD provided apparent benefits over the univariate method, which allowed information to be pooled across stations and resulted in improved precision of the estimates for the parameters and return levels of the distributions. The paper also discusses a method to construct informative priors empirically using historical data of the underlying process from weather characteristics of four pairs of surrounding weather stations at various distances. The results from the Bayesian analysis showed that posterior inference might be affected by the choice of priors that were used to formulate the informative priors. From the results, it could be inferred that the Bayesian approach provides a satisfactory estimation strategy in terms of precision, compared with the frequentist approach, because it accounts for uncertainty in parameters and return level estimations.

中文翻译：

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使用双变量分布建模极端风速的依存结构：贝叶斯方法

在调查天气变量的极端情况时，很少有一个气象站来确定损害，极端情况可能是由多个气象站的综合行为引起的。为了研究极端风速的联合依赖关系，从频度法和贝叶斯方法考虑了双变量广义极值分布（BGEVD），以分析南非选定气象站逐分量每月最大风速的极值。在常客主义方法中，极值分布（EVD）的参数估计的可能性最大，而在贝叶斯方法中，马尔可夫链蒙特卡洛（MCMC）技术与Metropolis-Hastings算法结合使用。结果表明，当拟合极端天气变量的逐分量最大值时，BGEVD提供了明显优于单变量方法的好处，后者使信息可以跨站进行汇总，并提高了参数估计值的估计精度和分布的返回水平。本文还讨论了一种方法，该方法利用基础过程的历史数据根据四对周围气象站在不同距离的天气特征，使用基础过程的历史数据来构建信息先验。贝叶斯分析的结果表明，后验推论可能会受到用于形成信息先验的先验选择的影响。从结果中可以推断出，贝叶斯方法相比于频度方法在准确性方面提供了令人满意的估算策略，