Estimating wildlife abundance is fundamental for its effective management and conservation. A range of methods exist: total counts, plot sampling, distance sampling and capture-recapture based approaches. Methods have assumptions and their failure can lead to substantial bias. Current research in the field is focused not on establishing new methods but in extending existing methods to deal with their assumptions' violation. This thesis focus on incorporating animal movement into circular plot sampling (CPS) and point transect sampling (PTS), where a key assumption is that animals do not move while within detection range, i.e., the survey is a snapshot in time. While targeting this goal, we found some unexpected bias in PTS when animals were still and model selection was used to choose among different candidate models for the detection function (the model describing how detectability changes with observer-animal distance). Using a simulation study, we found that, although PTS estimators are asymptotically unbiased, for the recommended sample sizes the bias depended on the form of the true detection function. We then extended the simulation study to include animal movement, and found this led to further bias in CPS and PTS. We present novel methods that incorporate animal movement with constant speed into estimates of abundance. First, in CPS, we present an analytic expression to correct for the bias given linear movement. When movement is de ned by a diffusion process, a simulation based approach, modelling the probability of animal presence in the circular plot, results in less than 3% bias in the abundance estimates. For PTS we introduce an estimator composed of two linked submodels: the movement (animals moving linearly) and the detection model. The performance of the proposed method is assessed via simulation. Despite being biased, the new estimator yields improved results compared to ignoring animal movement using conventional PTS.

When investigating the dynamics of an animal population, a primary objective is to obtain reasonable estimates of abundance or population size. This thesis concentrates on the problem of obtaining point estimates of abundance from capture-recapture data and on how such estimation can be improved by using the method of plant-capture. Plant-capture constitutes a natural generalisation of capture-recapture. In a plant-capture study a pre-marked population of known size is added to the target population of unknown size. The capture-recapture experiment is then carried out on the augmented population. Chapter 1 considers the addition of planted individuals to target populations which behave according to the standard capture-recapture model M0. Chapter 2 investigates an analogous model based on sampling in continuous time. In each of these chapters, distributional results are derived under the assumption that the behaviour of the plants is indistinguishable from that of members of the target population. Maximum likelihood estimators and other new estimators are proposed for each model. The results suggest that the use of plants is beneficial, and furthermore that the new estimators perform more satisfactorily than the maximum likelihood estimators. Chapter 3 introduces, initially in the absence of plants, a new class of estimators, described as coverage adjusted estimators, for the standard capture-recapture model M[sub]h. These new estimators are shown, through simulation and real life data, to compare favourably with estimators that have previously been proposed. Plant-capture versions of these new estimators are then derived and the usefulness of the plants is demonstrated through simulation. Chapter 4 describes how the approach taken in chapter 3 can be modified to produce a new estimator for the analogous continuous time model. This estimator is then shown through simulation to be preferable to estimators that have previously been proposed.

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Means of drawing truly random samples from populations of trees distributed non-randomly in a plane are practically unknown. Only the technique of numbering all items and drawing from a list is commonly suggested. Two other techniques are developed, reducing plot size and selecting from a cluster with probability (1/M) where M is larger than the cluster size. The exact bias from some other selection schemes is shown by the construction of "preference maps". Methods of weighting the selection by tree height, diameter, basal area, gross volume, vertical cross-sectional area and combinations of diameter and basal area are described. None of them require actual measurement of the tree parameters. Mechanical devices and field techniques are described which simplify field application. The use of projected angles, such as are used in Variable Plot Sampling is central to most of these methods. Critical Height Sampling Theory is developed as a generalization of Variable Plot Sampling. The field problem is simply to measure the height to where a sighted tree is "borderline" with a relaskop. The average sum of these "critical heights" at a point multiplied by the Basal Area Factor of a prism gives a direct estimate of stand volume without the aid of volume tables or tree measurements. Approximation techniques which have the geometrical effect of changing the expanded tree shape are described. The statistical advantages of using the system were not found to be large, and the problems of measuring the critical height on nearby trees was severe. In general use there appears to be no advantage over standard techniques of Variable Plot Sampling, however in situations where no volume tables exist it may have application, and the problem of steep measurements angles to nearby trees can be overcome by using an optical caliper. The system can also overcome the problem of "ongrowth" for permanent sample plots. / Forestry, Faculty of / Graduate

"The purpose of this paper is to present two methods for proving that a statistical estimate is admissible and minimax. The Bayes method was introduced by Wald, and Theorems 2.2 and 2.3 illustrate the technique. The second way is due to Hodges and Lehmann and is based on a lower bound for the variance of an estimate. In Theorem 3.2 the Hodges-Lehmann method for proving admissibility is given. The last chapter is devoted to an extension of the Hodges and Lehmann technique to the Bhattacharyya bounds"--Introduction. / "August, 1954." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: A. V. Fend, Professor Directing Paper. / Includes bibliographical references (leaves 44-45).

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Call number: LD2668 .T4 1979 F73 / Master of Arts

Chan For Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 88-90). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Basic Concepts --- p.6 / Chapter 2.1 --- Binomial vs Inverse Sampling --- p.6 / Chapter 2.2 --- Equivalence / Non-inferiority Test --- p.7 / Chapter 3 --- Testing Procedures --- p.9 / Chapter 3.1 --- The Model --- p.9 / Chapter 3.2 --- Asymptotic Behaviors of the Estimators --- p.10 / Chapter 3.2.1 --- Asymptotic Test Statistic based on Unconditional Maximum Likelihood Estimate --- p.12 / Chapter 3.2.2 --- Asymptotic Test Statistic based on restricted maximum likelihood estimate --- p.13 / Chapter 3.3 --- Conditional Exact Procedures --- p.16 / Chapter 3.3.1 --- Non-test-statistic-based procedure --- p.17 / Chapter 3.3.2 --- Test-statistic-based procedure --- p.17 / Chapter 4 --- Simulation Study --- p.19 / Chapter 4.1 --- Simulation Results - Type I error rate --- p.21 / Chapter 4.1.1 --- Asymptotic Test Statistic based on Unconditional MLE . . --- p.21 / Chapter 4.1.2 --- Asymptotic Test Statistic based on Restricted MLE . . . . --- p.22 / Chapter 4.1.3 --- Non-test-statistic-based Conditional Exact Test --- p.23 / Chapter 4.1.4 --- Test-statistic-based Conditional Exact Test --- p.24 / Chapter 4.2 --- Simulation Results - Power --- p.25 / Chapter 4.2.1 --- Asymptotic Tests - Similarity and Difference between using Unconditional and Restricted MLE --- p.25 / Chapter 4.2.2 --- Conditional Exact Tests - Similarity and Difference be- tween using Non-test-statistic-based and Test-statistic-based Procedures --- p.30 / Chapter 4.2.3 --- Test-statistic-based Conditional Exact Tests - Similarity and Difference between using Unconditional and Restricted MLE --- p.31 / Chapter 5 --- Conclusion --- p.32 / Appendices --- p.36 / Chapter A. --- Simulation Result - Type I error rate --- p.36 / Chapter B. --- Simulation Result - Power value --- p.42 / Bibliography --- p.88

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