Gap-based inverse sampling

We present a new inverse sampling design for surveys of rare events, Gap-Based Inverse Sampling. In the design, sampling stops if after a predetermined interval, or gap, no new rare events are found. The length of the gap that follows after finding a rare event is used as a way of limiting sample effort. We present stopping rules using decisions based on the gap length, the total number of rare events found, and a fixed upper limit of survey effort. We illustrate the use of the design with stratified sampling of two biological populations. The design uses the intuitive behavior of a field biologist in stratified sampling, where if in a stratum nothing is found after a long search, the field surveyor would like to consider the stratum is empty and stop searching. Our design has appeal for surveying rare events (for example, a rare species) with stratified sampling where there are likely to be some completely empty strata.