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[update]) the most cited article in its journal, Communications in Statistics – Theory and Methods.
- Naus, J. I. (1982). "Approximations for Distributions of Scan Statistics". Journal of the American Statistical Association 77 (377): 177–183. doi:10.1080/01621459.1982.10477783. JSTOR 2287786.
- Naus, Joseph Irwin (1964). Clustering of random points in line and plane (Ph. D.). Retrieved 6 January 2014.
- Wallenstein, S. (2009). "Joseph Naus: Father of the Scan Statistic". Scan Statistics. pp. 1–25. doi:10.1007/978-0-8176-4749-0_1. ISBN 978-0-8176-4748-3.
- Glaz, J.; Naus, J.; Wallenstein, S. (2001). "Introduction". Scan Statistics. Springer Series in Statistics. pp. 3–9. doi:10.1007/978-1-4757-3460-7_1. ISBN 978-1-4419-3167-2.
- Kulldorff, Martin (1997). "A spatial scan statistic" (PDF). Communications in Statistics - Theory and Methods 26 (6): 1481–1496.
- "Most Cited Articles". Communications in Statistics - Theory and Methods. Retrieved 11 October 2015.
- SaTScan free software for the spatial, temporal and space-time scan statistics