A spatial scan statistic
Communications in Statistics: Theory and Methods
A scan statistic is commonly used to test if a one dimensional point process is purely random, or if any clusters can be detected. Here it is simultaneously extended in three directions; (i) a spacial scan statistic for the detection of clusters in a multi dimensional point process is proposed, (ii) the area of the scanning window is allowed to vary, (iii) the baseline process may be any inhomogenous Poisson process or Bernoulli process with intensity proportional to some known function. The main interest is in detecting clusters not explained by the baseline process. These methods are illustrated on an epidemiological data set, but there are other potential areas of application as well.