FS3: a random walk based free-form spatial scan statistic for anomalous window detection

Often, it is required to identify anomalous windows over a spatial region that reflect unusual rate of occurrence of a specific event of interest. A spatial scan statistic essentially considers a scan window, and identifies anomalous windows by moving the scan window in the region. While spatial scan statistic has been successful, earlier proposals suffer from two limitations: (i) They restrict the scan window to be of a regular shape (e.g., circle, rectangle, cylinder). However, the region of anomaly, in general, is not necessarily of a regular shape. (ii) They take into account autocorrelation among spatial data, but not spatial heterogeneity. As a result, they often result in inaccurate anomalous windows. To address these limitations, we propose a random walk based free-form spatial scan statistic (FS³). Application of FS³ on real datasets has shown that it can identify more refined anomalous windows with better likelihood ratio of it being an anomaly, than those identified by earlier spatial scan statistic approaches.