Accounting for false negatives in hotspot detection

摘要

Hotspot sampling designs are used in environmental sampling to identify the location of one (or more) contiguous regions of elevated contamination. These regions are known as hotspots. The problem of how to calculate the probability of detecting an elliptical hotspot using a rectangular or triangular grid of sampling points was addressed by Singer and Wickman in 1969. This approach presumed that any sample which coincided with a hotspot would detect the hotspot without error. However, for many sampling methodologies, there is a chance that the hotspot will not be detected even though it has been sampled directly--a false negative. We present a mathematical solution and a numerical algorithm which account for false negatives when calculating the probability of detecting hotspots that are circular in shape.