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研究生:陳梓庭
研究生(外文):Tzu-Ting Chen
論文名稱:在卜瓦松分配下母體總數之貝氏估計
論文名稱(外文):Bayesian Estimation of Population Size under Poisson Distribution
指導教授:黃文典黃文典引用關係
指導教授(外文):Wen-Dean Hwang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:35
中文關鍵詞:貝氏估計重複捕取
外文關鍵詞:capture-recaptureBayesian estimation
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在生態統計的領域裡,母體總數的估計已經是一門極為古老且重要的研究,其中重複捕取的抽樣設計已廣泛應用於封閉性母體的總數估計,本文將Schmittlein(1985)提出NBD/BB模式的假設應用於母體估計,我們考慮由貝氏觀點將重複捕取和捕取移去的抽樣設計下所得到的資料用來推估母體總數。本文主要結果是在Mt,Mh模式及捕取移去模式下,利用貝氏方法推導我們有興趣的事後分布且得到貝氏估計量並與傳統無母數估計量比較。
Estimation of population size is an oldest and most important study in ecological statistics. To estimate the size of a closed population, a capture-recapture sampling design can be widely used. In this paper we introduce NBD/BB model presented by Schmittlein(1985) and apply its assumption to the estimation of the population size. We consider from a Bayesian viewpoint inference about the size of population from data obtained by capture-recaptural and capture-removal sampling scheme. The main result of the paper is able to derive expression for posterior distribution that are of interest by using Bayesian method under Mt, Mh and capture-removal model and obtain the Baysian estimator ,then compare with nonparametric estimator.
1緒論5
2 Mt模式下之重複捕取7
2.1 Mt模式下之貝氏估計量7
2.2 Mt模式下之無母數估計量14
2.3模擬設計與結果15
3 Mh模式下之重複捕取16
3.1 Mh模式下之貝氏估計量16
3.2 Mh模式下之無母數估計量19
3.3模擬設計與結果21
4捕取移去模式下之研究22
4.1移去模式下之貝氏估計量22
4.2移去模式下之最大概似估計量26
4.3模擬設計與結果27
5結論與未來研究方向28
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