Group inverse sampling: An economical approach to inverse sampling

Inverse sampling is an adaptive design in the sense that the final sampling effort during a search for rare events will depend on what is found during the survey. Conventional inverse sampling (CIS) designs successively select individual sampling units to find, for example, the kth rare event. In real sampling situations, use of successive one‐by‐one sampling can be cost prohibitive. Here, we introduce an inverse sampling design that uses successive selection of groups instead of individuals, named group inverse sampling (GIS). An unbiased estimator and its variance estimator of the population mean are derived based on the Murthy estimator. CIS is a special case of the generalized design with group size equal to one. We simulate the GIS design to evaluate its efficiency using populations of rare freshwater mussels in West Virginia, USA. For cost consideration, we calculate distance traveled among the sampling units. Results show that GIS was more cost efficient than CIS in all cases. The group size for successive sampling (d) was the most influential design parameter for reducing cost and increasing precision. Also, GIS found more rare units with greater consistency compared to simple random sampling without replacement (SRS). An important characteristic of the GIS design is that sampling stops when the target number of rare units is found, which prevents unnecessary sampling and contrasts favorably with other adaptive designs such as adaptive cluster sampling.