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Handling sparse spatial data in ecological applications

Embleton, Nina Lois (2015)
Ph.D. thesis, University of Birmingham.

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Abstract

Estimating the size of an insect pest population in an agricultural field is an integral part of insect pest monitoring. An abundance estimate can be used to decide if action is needed to bring the population size under control, and accuracy is important in ensuring that the correct decision is made. Conventionally, statistical techniques are used to formulate an estimate from population density data obtained via sampling.

This thesis thoroughly investigates an alternative approach of applying numerical integration techniques. We show that when the pest population is spread over the entire field, numerical integration methods provide more accurate results than the statistical counterpart. Meanwhile, when the spatial distribution is more aggregated, the error behaves as a random variable and the conventional error estimates do not hold. We thus present a new probabilistic approach to assessing integration accuracy for such functions, and formulate a mathematically rigorous estimate of the minimum number of sample units required for accurate abundance evaluation in terms of the species diffusion rate. We show that the integration error dominates the error introduced by noise in the density data and thus demonstrate the importance of formulating numerical integration techniques which provide accurate results for sparse spatial data.

Type of Work:Ph.D. thesis.
Supervisor(s):Petrovskaya, Natalia
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:HA Statistics
QA Mathematics
S Agriculture (General)
Institution:University of Birmingham
ID Code:5840
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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