摘 要
對於具空間相關性型態的資料，建立合適空間模型解釋資料的空間變異是重要的問題。此外，如何以此空間模型為基礎同時探討一特殊事件發生前後的空間風險變化是本文關心的重點。因此本篇論文以空間階層貝氏模型(spatial hierarchical Bayesian model)及空間條件自迴歸模型(spatial conditional autoregressive model)為基礎提出聯合建模的方法，藉此評估特殊事件發生前後風險的空間變化趨勢。論文中利用馬可夫鏈蒙地卡羅(Markov chain Monte Carlo)的技巧進行模型參數估計，並透過蒙地卡羅樣本評估特殊事件發生後各地區風險上升的可能性。最後我們以發生於1999年9月21日的台灣集集地震資料進行實例分析。





關鍵字：條件自迴歸模型、馬可夫鏈蒙地卡羅、Metropolis-Hastings 演算法、空間階層貝氏模型

Abstract
Modeling spatial patterns and processes to assess the spatial variations of data over a study region is an important issue in many fields. In this thesis, we focus on investigating the spatial variations of earthquake risks after a main shock. Although earthquake risks have been extensively studied in the literature, to our knowledge, there does not exist a suitable spatial model for assessing this problem. Therefore, we propose a joint modeling approach based on spatial hierarchical Bayesian models and spatial conditional autoregressive models to describe the spatial variations in earthquake risks over the study region during two periods. A family of stochastic algorithms based on Markov chain Monte Carlo technique is then performed for posterior computations. The probabilistic issue for the changes of earthquake risks after a main shock is also discussed. Finally, the proposed method is applied to the earthquake records for Taiwan before and after the Chi-Chi earthquake.
Key words: Conditional autoregressive model, Markov chain Monte Carlo, Metropolis-Hastings algorithm, Spatial hierarchical Bayesian model

謝誌 i
摘 要 ii
Abstract iii
目 錄 iv
圖目錄 v
表目錄 v
第一章 研究背景與目的 1
第一節 研究背景 1
第二節 動機與目的 4
第二章 統計方法 8
第一節 空間統計模型 8
第二節 參數估計 11
第三章 真實資料分析 21
第一節 資料介紹 21
第二節 分析結果 22
第四章 結論與討論 31
參考文獻 32

圖目錄
圖一︰芮氏規模≥ 2.0 L M 地震散佈圖 6
圖二︰迴歸係數後驗樣本直方圖 25
圖三︰ 1μ 與2 μ 後驗樣本直方圖 25
圖四︰ 0 φ 、1φ 和2 φ 後驗樣本直方圖 26
圖五︰ 20 σ 、21 σ 和22 σ 後驗樣本直方圖 27
圖六︰exp{ + }; i = 1, ,500 ; k = 1,2, ki ki … μ δ 後驗樣本的平均數曲面 29
圖七︰ ( ( , ) ) 1 2 P r R R r i i > 的估計值 30
表目錄
表一︰ 1 Y 、2 Y 、i SOR1 與i SOR2 的分布 22
表二︰模型參數後驗樣本的統計推論 28

參考文獻
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