Adaptive Cluster Sampling

Abstract

In many real-world sampling situations, researchers would like to be able to adaptively increase sampling effort in the vicinity of observed values that are high or otherwise interesting. This article describes sampling designs in which, whenever an observed value of a selected unit satisfies a condition of interest, additional units are added to the sample from the neighborhood of that unit. If any of these additional units satisfies the condition, still more units may be added. Sampling designs such as these, in which the selection procedure is allowed to depend on observed values of the variable of interest, are in contrast to conventional designs, in which the entire selection of units to be included in the sample may be determined prior to making any observations. Because the adaptive selection procedure introduces biases into conventional estimators, several estimators are given that are design unbiased for the population mean with the adaptive cluster designs of this article; that is, the unbiasedness does not depend on any assumptions about the population. The Rao-Blackwell method is used to obtain improved unbiased estimators; because of the incompleteness of the minimal sufficient statistic, more than one of these improved estimators are obtained. Simple criteria are given determining when adaptive cluster sampling strategies are more efficient than simple random sampling of equivalent sample size. Motivation for the designs in this article is provided by a wide variety of sampling situations in fields such as ecology, geology, and epidemiology. For example, in a survey of a rare bird species, once individuals of the species are detected, additional observations at nearby sites often reveal more individuals. In a study of a contagious disease, the addition to the sample of close contacts of infected individuals reveals a higher than average incidence rate. The results and examples in this article show that adaptive cluster sampling strategies give lower variance than conventional strategies for certain types of populations and, in particular, provide an extremely effective way of sampling rare, clustered populations.