PoT-GEV模型（Olafsdottir et al. 2021）是一種結合廣義極值（generalized extreme value; GEV）分佈和峰值超過閾值（peaks over threshold; PoT）方法的統計模型，近期已被廣泛應用於極端值分析。PoT-GEV模型用於擬合最大值序列資料，可進一步地評估極端值資料發生的強度和頻率之趨勢。當PoT-GEV模型用於分析氣候和環境的資料時，將空間和時間效應納入模型中是不可或缺的。因此，本論文提出一個新穎的時空階層PoT-GEV模型，此模型使用潛在高斯隨機過程描述PoT-GEV模型的參數用以捕捉資料的空間訊息，同時結合時間相關的協變量用以考慮時間效應。此外，我們採用拉普拉斯近似（Laplace approximation）來取代貝式方法中馬可夫鏈蒙地卡羅（MCMC）的參數估計方法，有效地提高計算效率。我們透過各式的模擬情境來展示時空階層PoT-GEV模型的有效性，同時分析台灣的降雨數據和PM2.5濃度來說明所提方法的實用性。;The PoT-GEV model by Olafsdottir et al. (2021) is a statistical model that combines the generalized extreme value (GEV) distribution with the peaks over threshold (PoT) approach, has been used in extreme value analysis. This model is used to fit block maximum data and can estimate trends in their intensity and frequency. Incorporating spatial and temporal effects into the PoT-GEV model is essential when analyzing climate and environmental data sets. In this research, we propose a novel spatio-temporal hierarchical PoT-GEV model. This model captures spatial information via a latent Gaussian process applied to the PoT-GEV parameters and incorporates time covariates for temporal effects. Furthermore, we employ the Laplace approximation method as an effective alternative to the Markov chain Monte Carlo (MCMC) parameter estimation techniques, aimed at enhancing computational efficiency. We demonstrate the efficacy of our proposed methodology through simulation studies covering various scenarios, with illustrations provided through the analysis of rainfall data and PM2.5 concentrations from Taiwan.
