Abstract
Section 43.1 introduces the concept of scan statistics and overviews types used to localize unusual clusters in continuous time or space, in sequences of trials or on a lattice. Section 43.2 focuses on scan statistics in one dimension. Sections 43.2.2 and 43.2.3 deal with clusters of events in continuous time. Sections 43.2.4 and 43.2.5 deal with success clusters in a sequence of discrete binary (s-f) trials. Sections 43.2.6 and 43.2.7 deal with the case where events occur in continuous time, but where we can only scan a discrete set of positions. Different approaches are used to review data when looking for clusters (the retrospective case in Sects. 43.2.2, 43.2.5, 43.2.6), and for ongoing surveillance that monitors unusual clusters (the prospective case in Sects. 43.2.2, 43.2.3, 43.2.7). Section 43.2.7 describes statistics used to scan for clustering on a circle (are certain times of the day or year more likely to have accidents?). Section 43.3 describes statistics used to scan continuous space or a two-dimensional lattice for unusual clusters. Sections 43.2 and 43.3 focus on how unusual the largest number of events within a scanning window is. Section 43.4.1 deals with scanning for unusually sparse regions. In some cases the researcher is more interested in the number of clusters, rather than the size of the largest or smallest, and Sect. 43.4.2 describes results useful for this case. The double-scan statistic of Sect. 43.4.3 allows the researcher to test for unusual simultaneous or lagged clustering of two different types of events. Section 43.4.4 describes scan statistics that can be used on data with a complex structure.