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研究生:楊欣洲
研究生(外文):Hsin-Chou Yang
論文名稱:馬可夫鏈模式與核平滑法在重複捕取實驗上的應用
論文名稱(外文):The Applications of Markov Chain Models and Kernel Smoothing in Capture-Recapture Experiments
指導教授:趙蓮菊趙蓮菊引用關係
指導教授(外文):Anne Chao
學位類別:博士
校院名稱:國立清華大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:144
中文關鍵詞:重複捕取總數估計行為反應個體異質馬可夫鏈核平滑法估計方程式最佳帶寬
外文關鍵詞:capture-recapturepopulation size estimationbehavior responseindividual heterogeneityMarkov chainkernel smoothingestimating equationoptimal bandwidth
相關次數:
  • 被引用被引用:1
  • 點閱點閱:279
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  • 下載下載:42
  • 收藏至我的研究室書目清單書目收藏:1
本文主要討論在重複捕取實驗 (capture-recapture experiment) 下,母體總數 (population size) 的估計問題。文中分別針對封閉型母體 (closed population) 與開放型母體 (open population),提出參數估計方法及估計性質。
在封閉型母體中,本文提出以馬可夫鏈模式 (Markov chain model) 來處理影響捕取機率的三個變異來源:行為反應 (behavior response)、時間效果 (time effect) 與個體差異 (individual heterogeneity)。對於行為反應的處理,傳統行為反應模式認為,捕取機率與之前是否被捕有關。有別於傳統行為反應模式,本文提出以馬可夫相關性 (Markovian dependence) 來架構樣本間的相關,認為已知過去捕取歷史下,捕取機率只與前次是否被捕有關。當時間效果也存在時,此時捕取機率為時間的函數,
可利用非均勻 (nonhomogeneous) 馬可夫鏈同時處理時間效果與行為反應。對於個體差異現象,文中是利用具有隨機效應的捕取機率來解釋,或是透過觀察到的共變量 (covariate) 訊息來估計各動物的捕取機率,分別提出混合效果模式和共變量模式來分析。
在各模式下,針對主要關心的母體總數以及其他相關參數,提出最大概似估計,並討論其估計性質。文中以兩組資料作為實例,Nichols et al. (1984) 分析的北美田鼠資料與 Otis et al. (1978) 的老鼠資料,說明估計方法的實際應用。同時,為了瞭解所提出估計式的表現,文中採用模擬分析加以探討。透過模擬結果發現,在滿足馬可夫相關性的情形下,馬可夫鏈模式確實可以輔助傳統行為模式,降低估計偏差 (bias) 與均方根誤差(root mean squared error),並且得到滿意的涵蓋率 (coverage)。
在開放型母體中,本文主要利用核平滑法 (kernel smoothing approach) 來處理長期性重複捕取實驗中,捕取樣本 (sampling occasions) 很多的問題。對於母體不再滿足封閉性的假設,文中分別提出局部常數模式 (local constant model) 和局部多項式模式 (local polynomial model),逐步放鬆封閉性的要求。對於存在動物個體間的異質現象,模式中將動物的捕取機率視為一組來自未知分配的隨機樣本,此分配由前兩階動差 (moment) 決定,透過隨機性來模式化個體差異的影響,並透過結合樣本涵蓋 (sample coverage) 與估計方程式(estimating equation) 的方法,估計母體總數及其他相關參數,同時推廣了 Huggins 與 Yip (1999) 處理時間效果的估計方法和Chao et al. (2001) 處理封閉母體的估計方法。
對於開放母體總數的變異數估計,除了提出大樣本近似估計外,也介紹如何利用重抽法 (bootstrap method) 的概念來估計變異數,進而得到信賴區間估計。對於核平滑估計中常遇到的最佳帶寬 (optimal bandwidth) 的選取問題,也可利用重抽法來解決,這樣的方法概念上很簡單,電腦計算時間也合理。本部分以香港米埔鳥類保育區的鷦鶯資料,和澳洲南方費雪島上的短尾海鷗資料作為實例,說明所提出的估計方法的實際應用。文中同時藉由一些模擬研究來瞭解核平滑估計式的表現。由模擬分析中發現,在個體異質性真的存在時,所提出的估計方法的確可以改善只考慮時間效果的估計方法,得到較小的均方根誤差。
第一章 緒論
第二章 封閉型模式
2.1 符號介紹
2.2 文獻回顧
2.3 研究動機
2.4 傳統時間及行為模式
2.5 時間及行為馬可夫鏈模式
2.5.1 均勻馬可夫鏈模式
2.5.2 限制模式
2.5.3 穩定模式
2.5.4 非均勻馬可夫鏈模式
2.6 時間、行為及個體差異模式
2.6.1 混合效果模式一:條件法
2.6.2 混合效果模式二:邊際法
2.6.3 混合效果模式三:共變量模式
2.7 實例分析
2.7.1 實例分析一:北美田鼠資料(沒有共變量)
2.7.2 實例分析二:老鼠資料(有共變量)
2.8 模擬分析
第三章 開放型模式
3.1 符號介紹
3.2 文獻回顧
3.3 研究動機
3.4 局部常數模式
3.4.1 三個未知量的估計
3.4.2 母體總數估計
3.5 局部多項式模式
3.5.1 三個未知量的估計
3.5.2 母體總數估計
3.6 變異數估計與最佳帶寬的決定
3.6.1 變異數與信賴區間的估計
3.6.2 最佳帶寬的決定
3.7 實例分析
3.7.1 實例分析一:灰頭鷦鶯資料
3.7.2 實例分析二:短尾海鷗資料
3.8 模擬分析
第四章 結論與討論
附錄
A 樣本相關性的探討
B 馬可夫鏈之假設檢定
C 局部多項式下的估計方程式
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