Strip Transect Sampling to Estimate Object Abundance in Homogeneous and Non-homogeneous Poisson Fields: a Simulation Stu
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Strip Transect Sampling to Estimate Object Abundance in Homogeneous and Non-homogeneous Poisson Fields: a Simulation Study of the Effects of Changing Transect Width and Number Timothy C. Coburn · Sean A. McKenna · Hirotaka Saito Received: 26 April 2008 / Accepted: 10 June 2008 / Published online: 16 July 2008 © International Association for Mathematical Geology 2008
Abstract This paper investigates the use of strip transect sampling to estimate object abundance when the underlying spatial distribution is assumed to be Poisson. A design-based rather than model-based approach to estimation is investigated through computer simulation, with both homogeneous and non-homogeneous fields representing individual realizations of spatial point processes being considered. Of particular interest are the effects of changing the number of transects and transect width (or alternatively, coverage percent or fraction) on the quality of the estimate. A specific application to the characterization of unexploded ordnance (UXO) in the subsurface at former military firing ranges is discussed. The results may be extended to the investigation of outcrop characteristics as well as subsurface geological features. Keywords Strip transect sampling · Unexploded ordnance · Object abundance · Spatial Poisson field · Design-based computer simulation
T.C. Coburn () Department of Management Science, Abilene Christian University, P.O. Box 29315, Abilene, TX 79699, USA e-mail: [email protected] S.A. McKenna Geoscience Research and Applications Group, Sandia National Laboratories, Albuquerque, NM 87185, USA e-mail: [email protected] H. Saito Department of Ecoregion Science, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183-8509, Japan e-mail: [email protected]
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Math Geosci (2009) 41: 51–70
1 Introduction Physical, biological, and environmental phenomena often occur in nature as manifestations of spatial point processes, and the Poisson distribution is generally a reasonable model for their rates of occurrence. Many scientific problems involve the estimation of the rate of occurrence (intensity) or abundance of some population or species of interest through sampling studies. A common field-based survey approach is to record measurements along a series of randomly-situated transects, estimating the total number of objects in the entire field, or their rate of occurrence, from the resulting data. While the number, size, and shape of the transects necessary to obtain high quality estimates of object abundance is always of concern, the transect sampling design is sometimes developed in a subjective way to provide “adequate coverage,” to facilitate ease of data collection, or to identify some presumed spatial pattern, rather than to optimize statistical performance. Using a design-based rather than model-based framework, this paper specifically addresses the effects of changing the number of transects and the transect width (or alternatively, coverage percent or fraction) under random sampling on the accuracy and precision of e
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