Information weighted sampling for detecting rare items in finite populations with a focus on security

Abstract

Frequently one has to search within a finite population for a single particular individual or item with a rare characteristic. Whether an item possesses the characteristic can only be determined by close inspection. The availability of additional information about the items in the population opens the way to a more effective search strategy than just random sampling or complete inspection of the population. We will assume that the available information allows for the assignment to all items within the population of a prior probability on whether or not it possesses the rare characteristic. This is consistent with the practice of using profiling to select high risk items for inspection. The objective is to find the specific item with the minimum number of inspections. We will determine the optimal search strategies for several models according to the average number of inspections needed to find the specific item. Using these respective optimal strategies we show that we can order the numbers of inspections needed for the different models partially with respect to the usual stochastic ordering. This entails also a partial ordering of the averages of the number of inspections. Finally, the use, some discussion, extensions, and examples of these results, and conclusions about them are presented.