AI 中文总结
本文提出基于extremMHMC R包的贝叶斯框架，结合约束先验与HMC算法，用于GEV分布参数估计，可降低小样本下的RMSE，经9715站点数据验证适用于大规模雪荷载分析。
AI 中文摘要
本文开发了一种贝叶斯框架，用于估计年最大积雪量引发的雪荷载的广义极值（GEV）分布参数，使用了本文开发的extremMHMC R包中实现的哈密顿蒙特卡洛（HMC）算法。该方法的关键在于使用适用于雪荷载场景的强先验分布作为形状参数，这有助于在小样本量情况下确保年最大积雪量分布参数估计的鲁棒性。这种鲁棒性是确保依赖GEV分布的结构可靠性分析产生符合物理实际的雪荷载估计的关键。强先验分布的信息来源于现有的极端降雨和降雪研究，其创新之处在于使用双曲正切函数在低雪和高雪工况之间转换先验分布参数。该方法使强先验方法具有全局适用性，同时保持物理真实性。此外，模拟研究证实，与频率学派方法相比，该方法的形状参数估计的均方根误差（RMSE）有所降低，尤其在小样本量情况下效果显著。最后，使用来自9715个站点的真实世界数据进一步证明了所提出的贝叶斯框架大规模应用的可行性。
英文摘要
This paper develops a Bayesian framework to estimate the parameters of the Generalized Extreme Value (GEV) distribution for the weight induced by annual maximum accumulations of snow, referred to as the snow load, using a Hamiltonian Monte Carlo (HMC) algorithm as implemented in the \enquote{extremMHMC} R package developed alongside this paper. Key to the approach is the use of strong prior distributions for the shape parameter that are appropriate in the context of snow loads, which helps to ensure robustness in the distribution parameter estimates for annual maximum snow loads despite small sample sizes. This robustness is key to ensuring that structural reliability analyses, which rely on the GEV distribution, produce physically realistic estimates of snow loads. Information on strong prior distributions is derived from existing studies on extreme rainfall and snowfall, with the novel use of hyperbolic tangent functions to transition the prior distribution parameters between low and high snow regimes. This approach enables global applicability of the strong prior approach while maintaining physical realism. Additionally, simulation studies confirm a reduction in Root Mean Square Error (RMSE) of the shape parameter estimate compared to frequentist methods, particularly for small sample sizes. Finally, a real-world application using a data from 9715 stations further demonstrates the feasibility of the proposed Bayesian framework for large scale implementation.
Commentsunder review, 10 figures
