Adaptive Cluster Sampling: Designs with Primary and Secondary Units

TLDR: In this article, an initial probability sample is selected and, whenever the observed value of the variable of interest satisfies a given condition, units in the neighborhood of that observation are added to the sample.

Abstract: SUMMARY In adaptive cluster sampling designs, an initial probability sample is selected and, whenever the observed value of the variable of interest satisfies a given condition, units in the neighborhood of that observation are added to the sample. In this paper, the initial design is selected in terms of primary units, while subsequent sampling is in terms of secondary units. Such initial designs include systematic sampling, strip sampling, and other forms of classical cluster sampling. But because of the subsequent addition to the sample of secondary units in the neighborhood of any (secondary) unit that satisfies the condition of interest, the final "clusters" of units obtained through the procedure may be quite different in shape from the initial primary units. The methods described in this paper apply to such sampling situations as whale surveys in which the research vessel temporarily leaves the selected transect to close in on sighted whales, surveys of rare bird species in which initial observations are made at systematically selected sites and additional observations are made in the vicinity of any site at which sufficiently high abundance is observed, and aerial walrus surveys in which the aircraft searches to either side of the preselected transect line whenever a congregation of animals is encountered. Because conventional estimators of the population mean and total are biased with such a procedure, estimators that are unbiased under the adaptive designs are presented in this paper. Variance formulae and unbiased estimators of variance are also given. The designs are illustrated using a point pattern representing locations of individuals or objects in a spatially aggregated population; for such a population, the adaptive designs can be substantially more efficient than their conventional counterparts.