In statistics, a scan statistic or window statistic is a problem relating to the clustering of randomly positioned points. An example of a typical problem is the maximum size of a cluster of points on a line or the longest series of successes recorded by a moving window of fixed length.
Joseph Naus first published on the problem in the 1960s, and has been called the "father of the scan statistic" in honour of his early contributions. The results can be applied in epidemiology, public health and astronomy to find unusual clusters of events.
It was extended by Martin Kulldorff to multi-dimensional settings and varying window sizes in a 1997 paper, which is (as of 11 October 2015) the most cited article in its journal, Communications in Statistics – Theory and Methods.