论文标题
块最大值方法的经验贝叶斯推断
Empirical Bayes inference for the block maxima method
论文作者
论文摘要
块最大值方法是极端价值分析的最流行的方法之一，具有独立且相同分布的观测值，在吸引极值分布的域中。在这种情况下，缺乏对贝叶斯推论的严格研究限制了其用于极端统计分析的用途。在本文中，我们提出了一种经验贝叶斯程序，以推断《最大值法》及其相关数量。我们表明，数据分布的尾部索引和返回水平（代表未来极端发作的代表）的后验分布满足了许多重要的理论特性。这些保证了后验推断的可靠性，并扩展到后验预测分布，这是贝叶斯概率预测中的关键工具。后验计算很容易通过有效的自适应算法类型的算法获得。模拟显示其出色的推论性能已经具有适度的样本量。我们的提案的实用性展示了分析大西洋盆地飓风产生的极端风。
The block maxima method is one of the most popular approaches for extreme value analysis with independent and identically distributed observations in the domain of attraction of an extreme value distribution. The lack of a rigorous study on the Bayesian inference in this context has limited its use for statistical analysis of extremes. In this paper we propose an empirical Bayes procedure for inference on the block maxima law and its related quantities. We show that the posterior distributions of the tail index of the data distribution and of the return levels (representative of future extreme episodes) satisfy a number of important theoretical properties. These guarantee the reliability of posterior-based inference and extend to the posterior predictive distribution, the key tool in Bayesian probabilistic forecasting. Posterior computations are readily obtained via an efficient adaptive Metropolis-Hasting type of algorithm. Simulations show its excellent inferential performances already with modest sample sizes. The utility of our proposal is showcased analysing extreme winds generated by hurricanes in the Atlantic basin.
