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SPATIALLY-BALANCED SAMPLING OF NATURAL RESOURCES
Citation:
Stevens, D. L. AND A R. Olsen. SPATIALLY-BALANCED SAMPLING OF NATURAL RESOURCES. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION. American Statistical Association, Alexandria, VA, 99(465):262-278, (2004).
Description:
The spatial distribution of a natural resource is an important consideration in designing an efficient survey or monitoring program for the resource. Generally, sample sites that are spatially-balanced, that is, more or less evenly dispersed over the extent of the resource, will be more efficient than simple random sampling. We review a unified strategy for selecting spatially-balanced probability samples of natural resources. The technique is based on creating a function that maps 2-dimensional space into 1-dimensional space, thereby defining an ordered spatial address. We use a restricted randomization to randomly order the addresses, so that systematic sampling along the randomly-ordered linear structure results in a spatially well-balanced random sample. Variable inclusion probability, proportional to an arbitrary positive ancillary variable, is easily accommodated. The basic technique selects points in a 2-dimensional continuum, but is also applicable to sampling finite populations or 1-dimensional continua embedded in 2-space. An extension of the basic technique gives a way to order the sample points so that any set of consecutively-numbered points is in itself a spatially-well-balanced sample. This latter property is extremely useful in adjusting the sample for the frame imperfections common in environmental sampling.