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研究生： 蘇郁珺
Su, Yu-Chun
論文名稱： 基因多樣性新指標之貝氏估計量的研究
The Bayes Estimator for a New Class of Gene Diversity Indices
指導教授： 馬瀰嘉
Ma, Mi-Chia
學位類別： 碩士
Master
系所名稱： 管理學院 - 統計學系
Department of Statistics
論文出版年： 2011
畢業學年度： 99
語文別： 英文
論文頁數： 59
中文關鍵詞： 生物多樣性 、辛普森歧異度指標 、香濃指標 、核苷酸多樣性 、貝式估計量 、Horvitz-Thompson估計量
外文關鍵詞： Biodiversity, Simpson’s diversity index, Shannon’s diversity index, Nucleotide diversity index, Bayes estimator, Horvitz-Thompson estimator
相關次數： 點閱：147  下載：1 
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    • 如何衡量基因歧異度以及如何對這些歧異度指標做估計，在文獻中，已經有許多學者探討。本文中，提出一個衡量基因歧異度的整合性指標，分別以不同的參數組合而定義出不同的歧異度指標，其中，此整合性指標包含了三個常被用來衡量基因歧異度的指標，如辛普森歧異度指標、香濃指標和核苷酸多樣性指標等。並且，利用貝氏估計量的方法進一步推導出新的整合性指標在基因型種類未知和已知之下的估計量，並證得這些估計量具有漸近一致的性質。並以模擬的方法進一步驗證漸近一致的性質以及將不同估計量拿來做相互比較

    How to measure and estimate the allelic diversity have been introduced by many scholars in the literatures. A new class of the allelic diversity measurements is proposed in this article. The widely used measurements such as Simpson’s diversity index, Shannon’s entropy and Nucleotide diversity index can be a special case of the new class with different parameters. Moreover, we use Bayesian approach to derive the Bayes estimator of the new diversity indices under known or not cases for the number of allelic types. We then prove the asymptotic consistency of these estimators. A simulation study is also conducted to compare the convergence rate between different parameters and the performance of these estimators.

    Chapter 1. Introduction 1 Chapter 2. Literature Review 4 2.1 Three diversity indices 4 2.2 Measurements of Diversity 6 2.2.1 Maximum Likelihood Estimator 6 2.2.2 Sample Coverage 8 2.2.3 Horvitz-Thompson Estimator 10 2.2.4 Bayes Estimator of Shannon index 12 Chapter 3. Proposed Methods 15 3.1 A new class of diversity indices 15 3.2 Bayes estimator of diversity indices class 16 3.2.1 S is known 16 3.2.2 S is unknown 18 3.3 The consistency of proposed index 21 Chapter 4. Real Example and Simulation Study 23 4.1 Real Example 23 4.2 Simulation design 28 4.3 Simulation Result 31 Chapter 5. Conclusion 36 Reference 37 Appendix A 40 Appendix B 44

    1. Basharin, G.P. (1959) “On a statistical estimate for the entropy of a sequence of independent random variable.” Theory of Probability and Its Applications, 4, 333-6.
    2. Brower J.E., Zar J.H., von Ende C.N. (1998). Field and Laboratory Methods for General Ecology. Boston: McGraw-Hill
    3. Casella, G., and Berger, R.L. (2002). Statistical Inference. 2nd edition. Thomson Learning, Australia.
    4. Chao, A. and Shen T.-J. (2003) Nonparametric estimation of Shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10, 429-43.
    5. Chao, A. and Lee, S.-M. (1992) Estimating the number of classes via sample coverage. Journal of the American Statistical Association, 87, 210-17.
    6. Chao, A., Hwang, W.-H., Chen, Y.-C., and Kuo, C.-Y. (2000) Estimating the number of shared species in two communities. Statistica Sinica, 10, 227-46.
    7. Chao, A., Ma, M.-C., and Yang, M.C.K. (1993) Stopping rules and estimation for recapture debugging with unequal failure rates. Biometrika, 80, 193-201.
    8. Chen, M. H. (2004) Morphological Variation and Genetic Diversity of Taiwan Ring-necked Pheasant Phasianus colchicus formosanus. Doctoral thesis, NTU. http://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dnclcdr&s=id=%22092NTU05360013%22.&searchmode=basic
    9. DeGiorgio, M. and Rosenberg, N.A. (2009) An unbiased estimator of gene diversity in samples containing related individuals. Mol. Biol. Evol. 26: 501-512.
    10. Esty, W. (1986) The efficiency of Good’s nonparametric coverage estimator. The Annals of Statistics, 14, 1257-60.
    11. Gaston, K.J. and Spicer, J.I. (1998). Biodiversity: an introduction. 2nd edition.
    12. Hsieh, Y.H. (2010). Statistical Evaluation of Equivalence Test Based on the Genetic Diversity Index. Master thesis, NCKU. http://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/ccd=YVcWLr/record?r1=1&h1=0
    13. Horvitz, D.G. and Thompson, D.J. (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663-85.
    14. Hutcheson, K. and Shenton, L.R. (1974) Some moments of an estimate of Shannon’s measure of information. Communications in Statistics, 3, 89-94.
    15. Lin, T. Y. (2006) The Bayes Estimation of Shannon’s Index of Diversity. Master thesis, NCKU. http://etdncku.lib.ncku.edu.tw/ETD-db/ETD-search-c/view_etd?URN=etd-0704106-184840
    16. MacArthur, R.H. (1957) On the relative abundances of bird species. Proceedings of National Academy of Science, U.S.A., 43, 193-295.
    17. Nei M. (1973). Analysis of gene diversity in subdivided populations. Proc Natl Acad Sci USA. 70:3321–3323.
    18. Nei, M. (1987). Molecular Evolutionary Genetics. Columbia Univ. Press, New York.
    19. Nei, M. and Li, W.-H. (1979). Mathematical model for studying genetic variation in terms of restriction endonucleases. Proc. Natl.Acad. Sci. USA 76: 5269–5273.
    20. Nei, M. and Roychoudhury AK. (1974). Sampling variances of heterozygosity and genetic distance. Genetics 76: 379–390.
    21. Pielou, E.C. (1975) Ecological Diversity, Wiley, New York.
    22. Shannon, Claude E. & Warren Weaver (1949): A Mathematical Model of Communication. Urbana, IL: University of Illinois Press
    23. Simpson, E.H. (1949). Measurement of diversity. Nature 163:688–688.
    24. Zhang, Q.F and Allard, R.W (1986) Sampling variance of the genetic diversity index.Heredity 77:54-55.

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