The Kernel Spatial Scan Statistic
This work addresses a problem in fields like epidemiology and security by improving anomaly detection, though it is incremental as it builds on existing SSS methods.
The authors tackled the limitation of spatial scan statistics (SSS) in handling smooth spatial anomalies by proposing a continuous scan statistic using kernels, which efficiently detects anomalous regions with high statistical power.
Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in epidemiology, environmental monitoring, and homeland security. SSS provides a way to rigorously test for the existence of an anomaly and provide statistical guarantees as to how "anomalous" that anomaly is. However, these methods rely on defining specific regions where the spatial information a point contributes is limited to binary 0 or 1, of either inside or outside the region, while in reality anomalies will tend to follow smooth distributions with decaying density further from an epicenter. In this work, we propose a method that addresses this shortcoming through a continuous scan statistic that generalizes SSS by allowing the point contribution to be defined by a kernel. We provide extensive experimental and theoretical results that shows our methods can be computed efficiently while providing high statistical power for detecting anomalous regions.