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研究生: 許根寧
Shu, Ken-Ning
論文名稱: 以統計模擬研究母體總數之貝氏估計
Estimating the number of species through Bayesian method in Sampling-based approaches
指導教授: 黃文典
Hwang, Wen-Dean
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2003
畢業學年度: 91
語文別: 英文
論文頁數: 25
外文關鍵詞: Bayesian
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    Gibbs sampler and Data augmentation algorithms can be viewed as two alter-
    native sampling(or Monte Carlo)-based approaches to calculate the numerical
    estimates of marginal density distribution. This article is concerned with the
    estimation of the number of species in a population through a fully hierarchical
    Bayesian model and an empirical Bayes approach using two kinds of alternative
    sampling-based approaches proposed above. The proposed Bayesian estimators
    are based on Poisson random variables with mean that are distributed according
    to a prior distribution with unknown parameters.

    1 Introduction .............................................................2 2 Hierarchical Bayesian Approach ...........................................4 2.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Sampling Approaches ......................................................8 3.1 Gibbs Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 3.2 Data augmentation . . . . . . . . . . . . . . . . . . . . . . . . . . ..9 4 Empirical Bayes Methodology .............................................10 5 An application of Butter y Data .........................................12 6 Simulation Study ........................................................14 7 Capture and Recapture Model .............................................16 8 Discussion ..............................................................19 9 Reference ...............................................................20 10 Appendix ...............................................................24

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