本研究提出一套適用於極端降雨事件分析的空間貝氏階層統計模型，擴充了由Olafsdottir等人(2021)所提出的峰值超過閾值廣義極值分布(PoT-GEV)架構，以納入不同地點之間的空間相依性。模型中，極端事件發生的頻率、強度與尾部行為等參數皆被視為受潛在高斯過程控制的空間隨機效應，以有效反映各地降雨極端程度的差異。為了解決高維空間推論所帶來的計算負擔，本研究採用一種高效率的二階段貝氏推論方法。具體而言，先使用拉普拉斯近似來逼近隨機效應的後驗分布，再透過Metropolis-Hastings演算法於MCMC框架下對超參數進行抽樣。在模擬研究中，我們進一步探討閾值選擇對模型估計準確度與穩定性的影響。最後，本方法應用於臺灣地區的逐日格點降雨資料，聚焦分析颱風季節的極端降雨事件。結果顯示，本模型不僅能有效捕捉空間上的極端行為差異，也能嚴謹評估其不確定性，顯示其於環境風險評估與空間極端值分析中的應用潛力。;This study proposes a spatial Bayesian hierarchical modeling framework for analyzing extreme precipitation, extending the peaks-over-threshold generalized extreme value (PoT-GEV) model to account for spatial dependence across locations. The model treats the frequency, scale, and shape parameters of the PoT-GEV distribution as location-specific random effects governed by latent Gaussian processes, thereby capturing spatial heterogeneity in both the occurrence and intensity of extreme events. To address the computational challenges posed by high-dimensional spatial inference, we adopt a two-stage Bayesian estimation strategy. Specifically, the Laplace approximation is used to efficiently approximate the posterior distribution of random effects, while the hyperparameters are sampled using the Metropolis-Hastings algorithm within a Markov chain Monte Carlo (MCMC) framework. Through extensive simulation studies, we evaluate the impact of threshold selection on estimation accuracy and model robustness. The proposed approach is further applied to gridded daily rainfall data across Taiwan, focusing on typhoon-season extremes. Results demonstrate the model’s ability to capture spatial variation in return levels and quantify associated uncertainty, underscoring its potential for reliable environmental risk assessment under a spatial extremes framework.
