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Sampling TheoryFor the Ecological and Natural Resource Sciences$
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David Hankin, Michael S. Mohr, and Kenneth B. Newman

Print publication date: 2019

Print ISBN-13: 9780198815792

Published to Oxford Scholarship Online: December 2019

DOI: 10.1093/oso/9780198815792.001.0001

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Spatially balanced sampling

Spatially balanced sampling

(p.240) Chapter 12 Spatially balanced sampling
Sampling Theory

David G. Hankin

Michael S. Mohr

Ken B. Newman

Oxford University Press

In many ecological and natural resource settings, there may be a high degree of spatial structure or pattern to the distribution of target variable values across the landscape. For example, the number of trees per hectare killed by a bark beetle infestation may be exceptionally high in one region of a national forest and near zero elsewhere. In such circumstances it may be highly desirable or even required that a sample survey directed at estimation of total tree mortality across a forest be based on selection of random locations that have good spatial balance, i.e., locations are well spread over the landscape with relatively even distances between them. A simple random sample cannot guarantee good spatial balance. We present two methods that have been proposed for selection of spatially balanced samples: GRTS (Generalized Random Tessellation Stratified Sampling) and BAS (Balanced Acceptance Sampling). Selection of samples using the GRTS approach involves a complicated series of sequential steps that allows generation of spatially balanced samples selected from finite populations or from infinite study areas. Selection of samples using BAS relies on the Halton sequence, is conceptually simpler, and produces samples that generally have better spatial balance than those produced by GRTS. Both approaches rely on use of software that is available in the R statistical/programming environment. Estimation relies on the Horvitz–Thompson estimator. Illustrative examples of running the SPSURVEY software package (used for GRTS) and links to the SDraw package (used for BAS) are provided at http://global.oup.com/uk/companion/hankin.

Keywords:   GRTS, Generalized Random Tessellation Stratified Sampling (GRTS), Balanced Acceptance Sampling (BAS), Halton sequence, van der Corput sequence, spatial balance, Voronoi polygons

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