Title page for ETD etd-122206-133926

Document Type masters report

Author Name Uemura, Shinji

Email Address shinji1205b at aol.com

URN etd-122206-133926

Title Estimating the Number of Species in a Population

Degree MS

Department Mathematical Sciences

Advisors
Corinne Burgos, Advisor

Keywords
hierarchical bayesian model

Date of Presentation/Defense 2006-12-12

Availability unrestricted

Abstract
This paper is concerned with the estimation of the number of species in a population. This is a familiar problem in ecological studies. Many scientists and statisticians have studied this problem. The method in estimating the number of species can be used in many other areas such as estimating the number of author's vocabulary.
Many approaches have been proposed, some purely data-analytic and others based in sampling theory. We consider the latter case and focus on three methods in this paper. First one was based on the paper of Efron and Thisted [7]. Second one was given by Boneh, et. al. [4]. Third one was about Bayesian method and was proposed by Rodrigues, et. al. [22]. And we compare these methods using Mt. Kenya data and Mt. Mandalagan data.
As a result, the first two methods underestimate the number of species in the population for both data sets. The Bayesian method gives us more reasonable estimates and credible intervals. But we need to know the upper bound value beforehand, which is usually provided by an expert or analyst involved in the study. Thus, we need to construct another model which does not have to have the upper bound value for further research.

Files
uemura.pdf

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Document Type	masters report
Author Name	Uemura, Shinji
Email Address	shinji1205b at aol.com
URN	etd-122206-133926
Title	Estimating the Number of Species in a Population
Degree	MS
Department	Mathematical Sciences
Advisors	Corinne Burgos, Advisor
Keywords	hierarchical bayesian model
Date of Presentation/Defense	2006-12-12
Availability	unrestricted
Abstract This paper is concerned with the estimation of the number of species in a population. This is a familiar problem in ecological studies. Many scientists and statisticians have studied this problem. The method in estimating the number of species can be used in many other areas such as estimating the number of author's vocabulary. Many approaches have been proposed, some purely data-analytic and others based in sampling theory. We consider the latter case and focus on three methods in this paper. First one was based on the paper of Efron and Thisted [7]. Second one was given by Boneh, et. al. [4]. Third one was about Bayesian method and was proposed by Rodrigues, et. al. [22]. And we compare these methods using Mt. Kenya data and Mt. Mandalagan data. As a result, the first two methods underestimate the number of species in the population for both data sets. The Bayesian method gives us more reasonable estimates and credible intervals. But we need to know the upper bound value beforehand, which is usually provided by an expert or analyst involved in the study. Thus, we need to construct another model which does not have to have the upper bound value for further research.
Files	uemura.pdf