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題名 品種重複的無母數估計
Nonparametric Estimation of Species Overlap作者 林逢章
Lin, Feng-Chang貢獻者 余清祥
Yue, Ching-Syang Jack
林逢章
Lin, Feng-Chang關鍵詞 品種重複
species overlap
Jaccard index
NPMLE
delta-beta-binomial
bootstrap日期 1998 上傳時間 21-Apr-2016 09:54:50 (UTC+8) 摘要 關於描述兩個觀察地A和B相似的程度而言，生物品種是否相同是其中的一個切入點，因此品種重複（species overlap）便為描述兩觀察地相似度的一種指標。就一般的生物或生態研究而言，較常使用的品種重複指數為以品種數為計算基礎的 Jaccard index，公式為 ，其中 和 分別為觀察地A和B的總品種數，而 則為兩地的共同品種數，這樣的計算方式為Gower(1985) 歸類描述兩單位（unit）的相似度（similarity）中的一種。在我們的研究中，將令依觀察到的品種數及品種重複數所計算出的 Jaccard index 視為估計值，記為 ；若描述相似度時僅以品種為計算單位，而忽略個別品種的數量未免有資訊流失的情形，因此我們延伸 Jaccard index 指數而另立以個別品種數為計算單位的 N 指數，並以無母數最大概似估計法（Nonparametric Maximum Likelihood Estimator, NPMLE）估計 N 指數，記為 。另外，Smith, Solow 和 Preston (1996) 也提出利用 delta-beta-binomial 模型修正 Jaccard index 的低估（underestimate）情形，我們將此模型所推估的品種重複記為 ，因此我們的研究重點便在於以模擬實驗比較 、 和 在估計真正參數時的行為。
In describing the similarity between communities A and B, species overlap is one kind of measure. In ecology and biology, the Jaccard index (Gower, 1985) ,denoted , for species overlap is widely used and is useded as an estimation in our research. However, the Jaccard index is simply the proportion of overlapping species, that is those species appearing in more than one community, to unique species, that is those species appearing in only one community. However, this index ignores species proportion information, assigning equal weight to all species. We propose a new index, N, which includes proportion information and is estimated by a Nonparametric Maximum Likelihood Estimator (NPMLE), denoted . Smith et al. (1996) proposed a delta-beta-binomial model to improve underestimation of the Jaccard index, we denoted this estimator .參考文獻 中文書目王吉松，民88，以用字分析紅樓夢之作者問題，政治大學統計研究所碩士論文。趙蓮菊，民84，種類知多少--敬獻給為台灣環保努力的朋友們，數學傳播，19，1-7。吳育美，民86，大學圖書館工程類西文圖書館藏重複及特性之研究：以台大、清大、交大、成大為例，淡江大學教育資料科學研究所碩士論文。陳恆安，民83，台中市沿都市郊區梯度上動物分佈與物種豐度，東海大學生物學研究所碩士論文。彭起嘉，民85，塔塔加火災過後地區小型哺乳類之群聚生態研究，東海大學生物學研究所碩士論文。外文書目Abele, L. G. (1979). The community structure of coral-associated decapod crustaceans in a variable environment. In Ecological Process in Coastal Marine Systems：Marine Science 10, 265-287, Florida State University. New York：Plenum Press.Becker, A. R., Chambers, M. John and Allan R. Wilks. (1988)The new S language-a programming environment for data analysis and graphics. Wadsworth and Brooks, California.Bunge, J. and Fitzpatrick, M. (1993). Estimating the number species： A review. Journal of the American Statistical Association 88, 364-373.Casella, G. and Berger, L. R. (1990). Statistical inference. Duxbury, Belmont, California.Chao, A. (1981). On estimating the probability of discovering a new species, Annals of Statistics, 6, 1339-1342.Clayton, K. Murray and Frees, Edward W. (1987). Nonparametric estimation of the probability of discovering a new species, Journal of the American Statistical Association, 82, 305-311.Efron, Bradley and Thisted, Ronald (1976). Estimating the number of Unseen species： How many words did Shakespeare know？, Biometrika, 63, 435-477.Engen, S. (1978). Stochastic Abundance Models. London: Chapman and Hall.Good, I. J. (1953). On the population Frequencies of species and the estimation of population parameters, Biometrika, 40, 237-264.Gower, J. C. (1985). Measures of similarity, dissimilarity, and distance. In Encyclopedia of Statistical Sciences, Volume 5, S. Kotz and N. L. Johnson (eds.), 397-405. Wiely ,New York.Higgs A. J. and Usher, M. B. (1980) Should nature reserves be large or small？Nature, 285, 568-569.Lee, Joohoo (1989) On asymptotic for the NPMLE of the probability of discovering a new species and an adaptive stopping rule in two-stage searches, Ph.D. Thesis.Pielou, E. C. (1979) Ecological Diversity, Wiley, New York.Robbins, H. (1968) Estimating the total probability of the unobserved outcomes of an experiment, Annals of Mathematical Statistics, 39, 256-257.Starr, Norman (1979) Linear estimation of the probability of discovering a new species, Annals of Statistics, 7, 644-652.Smith, W., Solow, A. R. and Preston, P. E. (1996). An estimator of species overlap using a modified beta-binomial model, Biometrics, 52, 1472-1477.Yue, C. S. Jack (1994) Bayesian sequential tests for comparing species richness of two populations, Ph.D. Thesis. 描述 碩士
國立政治大學
統計學系
86354015資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002001555 資料類型 thesis dc.contributor.advisor 余清祥 zh_TW dc.contributor.advisor Yue, Ching-Syang Jack en_US dc.contributor.author (Authors) 林逢章 zh_TW dc.contributor.author (Authors) Lin, Feng-Chang en_US dc.creator (作者) 林逢章 zh_TW dc.creator (作者) Lin, Feng-Chang en_US dc.date (日期) 1998 en_US dc.date.accessioned 21-Apr-2016 09:54:50 (UTC+8) - dc.date.available 21-Apr-2016 09:54:50 (UTC+8) - dc.date.issued (上傳時間) 21-Apr-2016 09:54:50 (UTC+8) - dc.identifier (Other Identifiers) B2002001555 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85884 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 86354015 zh_TW dc.description.abstract (摘要) 關於描述兩個觀察地A和B相似的程度而言，生物品種是否相同是其中的一個切入點，因此品種重複（species overlap）便為描述兩觀察地相似度的一種指標。就一般的生物或生態研究而言，較常使用的品種重複指數為以品種數為計算基礎的 Jaccard index，公式為 ，其中 和 分別為觀察地A和B的總品種數，而 則為兩地的共同品種數，這樣的計算方式為Gower(1985) 歸類描述兩單位（unit）的相似度（similarity）中的一種。在我們的研究中，將令依觀察到的品種數及品種重複數所計算出的 Jaccard index 視為估計值，記為 ；若描述相似度時僅以品種為計算單位，而忽略個別品種的數量未免有資訊流失的情形，因此我們延伸 Jaccard index 指數而另立以個別品種數為計算單位的 N 指數，並以無母數最大概似估計法（Nonparametric Maximum Likelihood Estimator, NPMLE）估計 N 指數，記為 。另外，Smith, Solow 和 Preston (1996) 也提出利用 delta-beta-binomial 模型修正 Jaccard index 的低估（underestimate）情形，我們將此模型所推估的品種重複記為 ，因此我們的研究重點便在於以模擬實驗比較 、 和 在估計真正參數時的行為。 zh_TW dc.description.abstract (摘要) In describing the similarity between communities A and B, species overlap is one kind of measure. In ecology and biology, the Jaccard index (Gower, 1985) ,denoted , for species overlap is widely used and is useded as an estimation in our research. However, the Jaccard index is simply the proportion of overlapping species, that is those species appearing in more than one community, to unique species, that is those species appearing in only one community. However, this index ignores species proportion information, assigning equal weight to all species. We propose a new index, N, which includes proportion information and is estimated by a Nonparametric Maximum Likelihood Estimator (NPMLE), denoted . Smith et al. (1996) proposed a delta-beta-binomial model to improve underestimation of the Jaccard index, we denoted this estimator . en_US dc.description.tableofcontents 目錄第一章 導論 1.1 導論………………………………………….. 1 1.2 文獻回顧……………………………………. 8 1.2.1 發現新品種的機率--無母數最大概似估計法…… 9 1.2.2 品種重複的估計…………………………… 11 1.2.3 跋靴法…………………………………… 12第二章 NPMLE 的性質 2.1 J指數和N指數的關聯性.……………………… 14 2.2 性質的描述……………….…………………… 15第三章 計算與模擬 3.1 導論…………………………………………… 19 3.2 計算…………………………………………… 20 3.3 模擬…………………………………………… 24 3.3.1 平衡母體…………………………………… 24 3.3.2 非平衡母體………………………………… 36第四章 實例…………………………………………… 51第五章 結論與未來的研究方向 5.1 結論…………………………………………… 56 5.2 未來的研究方向………………………………… 58參考書目………………………………………………… 61 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002001555 en_US dc.subject (關鍵詞) 品種重複 zh_TW dc.subject (關鍵詞) species overlap en_US dc.subject (關鍵詞) Jaccard index en_US dc.subject (關鍵詞) NPMLE en_US dc.subject (關鍵詞) delta-beta-binomial en_US dc.subject (關鍵詞) bootstrap en_US dc.title (題名) 品種重複的無母數估計 zh_TW dc.title (題名) Nonparametric Estimation of Species Overlap en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 中文書目王吉松，民88，以用字分析紅樓夢之作者問題，政治大學統計研究所碩士論文。趙蓮菊，民84，種類知多少--敬獻給為台灣環保努力的朋友們，數學傳播，19，1-7。吳育美，民86，大學圖書館工程類西文圖書館藏重複及特性之研究：以台大、清大、交大、成大為例，淡江大學教育資料科學研究所碩士論文。陳恆安，民83，台中市沿都市郊區梯度上動物分佈與物種豐度，東海大學生物學研究所碩士論文。彭起嘉，民85，塔塔加火災過後地區小型哺乳類之群聚生態研究，東海大學生物學研究所碩士論文。外文書目Abele, L. G. (1979). The community structure of coral-associated decapod crustaceans in a variable environment. In Ecological Process in Coastal Marine Systems：Marine Science 10, 265-287, Florida State University. New York：Plenum Press.Becker, A. R., Chambers, M. John and Allan R. Wilks. (1988)The new S language-a programming environment for data analysis and graphics. Wadsworth and Brooks, California.Bunge, J. and Fitzpatrick, M. (1993). Estimating the number species： A review. Journal of the American Statistical Association 88, 364-373.Casella, G. and Berger, L. R. (1990). Statistical inference. Duxbury, Belmont, California.Chao, A. (1981). On estimating the probability of discovering a new species, Annals of Statistics, 6, 1339-1342.Clayton, K. Murray and Frees, Edward W. (1987). Nonparametric estimation of the probability of discovering a new species, Journal of the American Statistical Association, 82, 305-311.Efron, Bradley and Thisted, Ronald (1976). Estimating the number of Unseen species： How many words did Shakespeare know？, Biometrika, 63, 435-477.Engen, S. (1978). Stochastic Abundance Models. London: Chapman and Hall.Good, I. J. (1953). On the population Frequencies of species and the estimation of population parameters, Biometrika, 40, 237-264.Gower, J. C. (1985). Measures of similarity, dissimilarity, and distance. In Encyclopedia of Statistical Sciences, Volume 5, S. Kotz and N. L. Johnson (eds.), 397-405. Wiely ,New York.Higgs A. J. and Usher, M. B. (1980) Should nature reserves be large or small？Nature, 285, 568-569.Lee, Joohoo (1989) On asymptotic for the NPMLE of the probability of discovering a new species and an adaptive stopping rule in two-stage searches, Ph.D. Thesis.Pielou, E. C. (1979) Ecological Diversity, Wiley, New York.Robbins, H. (1968) Estimating the total probability of the unobserved outcomes of an experiment, Annals of Mathematical Statistics, 39, 256-257.Starr, Norman (1979) Linear estimation of the probability of discovering a new species, Annals of Statistics, 7, 644-652.Smith, W., Solow, A. R. and Preston, P. E. (1996). An estimator of species overlap using a modified beta-binomial model, Biometrics, 52, 1472-1477.Yue, C. S. Jack (1994) Bayesian sequential tests for comparing species richness of two populations, Ph.D. Thesis. zh_TW
