進階搜尋


   電子論文尚未授權公開,紙本請查館藏目錄
(※如查詢不到或館藏狀況顯示「閉架不公開」,表示該本論文不在書庫,無法取用。)
系統識別號 U0026-0807201119073900
論文名稱(中文) 基因多樣性新指標之貝氏估計量的研究
論文名稱(英文) The Bayes Estimator for a New Class of Gene Diversity Indices
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 99
學期 2
出版年 100
研究生(中文) 蘇郁珺
研究生(英文) Yu-Chun Su
學號 r26981075
學位類別 碩士
語文別 英文
論文頁數 59頁
口試委員 口試委員-陳俞成
口試委員-潘宏裕
指導教授-馬瀰嘉
中文關鍵字 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 
英文關鍵字 Biodiversity  Simpson’s diversity index  Shannon’s diversity index  Nucleotide diversity index  Bayes estimator  Horvitz-Thompson estimator 
學科別分類
中文摘要 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
英文摘要 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.
論文目次 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

參考文獻 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.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2021-12-31起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw