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Abstract
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The spatial scan statistics based on the Poisson and binomial models are the most common methods to detect spatial clusters in disease surveillance. These models rely on Monte-Carlo simulation which are time consuming. Moreover, frequently, datasets present over-dispersion which cannot be handled by them. Thus, we have the following goals. First, we propose irregularly shaped spatial scan for the Bell, Poisson, and binomial. The Bell distribution has just one parameter but it is capable of handling over-dispersed datasets. Second, we apply these scan statistics to big maps. A fast version, without Monte-Carlo simulation, for the proposed Poisson and binomial scans is introduced. Intensive simulation studies are carried out to assess the quality of the proposals. In addition, we show the time improvement of the fast scan versions over their traditional ones. Finally, we end the paper with an application on the detection of irregular shape small nodules in a medical image.
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