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標題: Good-Turing方法及其應用
Good-Turing Method and Its Application
作者: 黃文瀚
關鍵字: 數學類;基礎研究;Good-Turing estimation;有限母體;樣本涵蓋率;物種豐富度;finite population;sample coverage;species richness
假定一個母體由S個種類(或類別)所組成,今有n個個體由此母體隨機被取出。在一般情形下,通常會有一些種類在樣本不曾被觀察到,所以估計種類豐富度的分佈是一個蠻困難的工作。Good–Turing估計法(Good,1953, Biometrika)針對此一情形提供一種簡單但是相當有效的方法來推估種類豐富度的分佈。時至今日,這種方法已經在數個領域上成功地被使用,其中包括資訊擷取、計算語言學和生態多樣性的估計。然而,先前的研究大多數假設歸還性抽樣(或者從無限母體取樣)的情形,此一假設在許多應用上並不適合。本計劃將考慮在有限母體之不歸還抽樣的情形下,提出修正Good-Turing方法。我們將研究所提方法之大樣本性質。而且,我們也將研究其可能的推廣與應用(例如拼字校正,種類數估計,種類堆積物曲線和其他多樣性指標估計)。最後,本計劃也將以一些真實的有限母體評估所提方法的效用,此類有限母體包括來自熱帶森林科學的中心的一些森林的普查數據。

Suppose that a population consists of S species (classes), a random sample of size n is drawnfrom the population. In general, there is usually a set of species cannot be observed in thesample, thus it seems difficult to estimate the probability distribution of the species abundance.Good- Turing estimation (Good, 1953; Biometrika) provided a simple, yet effective, methodto predict the underlying probability distribution. To dates, the method has been appliedsuccessfully on several disciplines such as information retrieval, computing linguistics, andecological diversity estimation. Nevertheless, most of previous studies consider the case ofsampling with replacement (or sampling from an infinite population) that might be not true inmany applications.The project is going to propose an estimation method to predict the probability distribution ofspecies in a finite population. We will investigate the large sample properties of the proposedmethod. Furthermore, we would also address various extensions and applications includingspecies richness estimation, species accumulation curve, and other diversity index estimations.Finally, we will evaluate the proposed methods through several real finite populations thatinclude some forest data from the Center for Tropical Forest Science.
其他識別: NSC99-2118-M005-003-MY2
Appears in Collections:應用數學系所

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