论文标题
贝叶斯推断非参数极值理论
Bayesian Inference for Non-Parametric Extreme Value Theory
论文作者
论文摘要
实际上，由于样本量较低和研究罕见事件的模型不准确，因此很难对随机事件的极端值进行统计推断。如果有极值的先验知识可用，则可以应用贝叶斯统计数据以降低样本的复杂性，但这需要已知的概率分布。通过与分位数以极低的概率（按$ 10^{ - 2} $或更低的顺序）并依靠其渐近正态性，可以在不假定任何分布的情况下进行推理。尽管依靠渐近结果，但表明包含先前信息的贝叶斯框架可以减少将特定分位数估算到一定程度的准确性所需的观测值。
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be applied to reduce the sample complexity, but this requires a known probability distribution. By working with the quantiles for extremely low probabilities (in the order of $10^{-2}$ or lower) and relying on their asymptotic normality, inference can be carried out without assuming any distributions. Despite relying on asymptotic results, it is shown that a Bayesian framework that incorporates prior information can reduce the number of observations required to estimate a particular quantile to some level of accuracy.
