Sampling for Region-Aggregated Spatial Scan Statistics

Anomaly detection in geospatial data is a crucial tool in geographic information science (GIS), with applications ranging from national security to public-health surveillance to the study of societal disparities.

This work focuses on spatial scan statistics and addresses a key mismatch: spatial counts are typically aggregated into predefined regions (census tracts, zip codes, counties), whereas the most efficient scan algorithms operate on spatial point data.

The standard remedy -- collapsing each region to its centroid, as in widely used tools such as SaTScan -- is convenient but, as we show, discards the region's spatial extent and causes a significant loss in statistical power.

To resolve this, we propose a simple yet scalable fix: replace each spatial region with 20-50 points sampled uniformly from its geometry and spread the region's values evenly across them.

This approach improves statistical power while maintaining computational tractability.

A convergence analysis explains why so few samples per region suffice.

We recommend this sampling-based conversion as the default way to apply point-based spatial scan statistics to region-aggregated data for anomaly detection.