# The Kernel Spatial Scan Statistic

## TL;DR

This paper introduces a continuous kernel-based spatial scan statistic that improves anomaly detection by modeling gradual density decay, offering enhanced power and computational efficiency over traditional binary-region methods.

## Contribution

It generalizes the classical spatial scan statistic by incorporating kernel functions, enabling smoother and more realistic modeling of spatial anomalies.

## Key findings

- High statistical power demonstrated in experiments
- Efficient computation methods developed
- Outperforms traditional binary-region scan statistics

## Abstract

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.