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| 題 名 | The Bayes Estimation of Shannon's Diversity Index=SHANNON多樣性指數的貝氏估計量 |
|---|---|
| 作 者 | 林庭以; 馬瀰嘉; | 書刊名 | 中國統計學報 |
| 卷 期 | 51:1 2013.03[民102.03] |
| 頁 次 | 頁98-118 |
| 分類號 | 360.13 |
| 關鍵詞 | 生物多樣性; 豐富度; Shannon指標; 驗前分配; 貝氏估計量; Biodiversity; Abundance; Shannon's index; Prior distribution; Bayesian estimation; |
| 語 文 | 英文(English) |
| 中文摘要 | 由於人們長久以來對動植物棲息地恣意破壞,導致嚴重的生態危機,因此生物多樣性是近幾年來極為重要的生態研究主題。在本篇論文中,主要目的是假設物種總數未知下如何估計生物多樣性指標-Shannon指標。過去文獻指出最大概似估計量忽略了未出現在樣本中的物種之機率,所以估計量有低估的情形。在物種總數未知下,本文提出貝氏估計量,利用已知事前分配的訊息來對未出現在樣本中物種之機率加以估計。並以模擬結果來和文獻中不同方法比較在不同參數組合下的優劣情形。從模擬結果得知,當物種數和物種出現機率的驗前分配已知,偏誤修正貝氏估計量是Shannon指標的最佳估計量;當物種數未知時,在大樣本下代入物種數估計量的貝氏估計量,與趙和沈在2003年利用樣本涵蓋率所提出之Shannon指標估計量在均方誤不相上下。 |
| 英文摘要 | Biodiversity is an extremely important topic of ecology research in recent years, because mankind arbitrarily destroyed habitat of animals and plants to cause a serious ecological crisis. This paper is concerned with the estimation of Shannon's index of diversity when the number of species is unknown. The traditional maximum likelihood estimator underestimates the Shannon's index of diversity when there are many unseen species. We provide a Bayesian approach based on the relative abundances have a prior distribution when the number of species is unknown. A simulation study was conducted to empirically investigate and compare the pervious estimators and the proposed estimators for various scenarios. From the simulation results, when the number of species and the parameter of the prior distribution are known, the bias-corrected Bayes estimator is the best estimator of Shannon's index. When the number of species is unknown in practice, the simulation results show that Bayes estimator is competitive with the estimator of Chao and Shen (2003) when the sample size is large. |
本系統中英文摘要資訊取自各篇刊載內容。