Modeling the search for rare events: In search of sasquatch

The search for a species that may or may not be present is a problem in field biology. This problem may be as simple as determining whether or not a particular species of dragonfly has extended its range or as vague as the search for the elusive Sasquatch. In these searches, a primary concern is determining if the species does not exist in the search area or if the searcher has simply failed to find the species for which he is searching. To model this problem, a simple urn model is used. An urn with a small, unknown number of white marbles and a large number of black marbles is assumed. The white marbles represent searches in which the rare event is found. The black marbles represent unsuccessful searches. Two different prior distributions are assumed. The first is an exponential function and the second is a characteristic function. The posterior distribution is determined using Bayesian updating. A point of interest is the situation in which no white balls are drawn. In the first case, the expected value goes to zero, and the searcher can be confident that object in question does not exist. However, in the second case the expected value never goes to zero, always leaving the searcher with hope that the object exists.