Scalable spatial scan statistics through sampling

Abstract

Finding anomalous regions within spatial data sets is a central task for biosurveillance, homeland security, policy making, and many other important areas. These communities have mainly settled on spatial scan statistics as a rigorous way to discover regions where a measured quantity (e.g., crime) is statistically significant in its difference from a baseline population. However, most common approaches are inefficient and thus, can only be run with very modest data sizes (a few thousand data points) or make assumptions on the geographic distributions of the data. We address these challenges by designing, exploring, and analyzing sample-then-scan algorithms. These algorithms randomly sample data at two scales, one to define regions and the other to approximate the counts in these regions. Our experiments demonstrate that these algorithms are efficient and accurate independent of the size of the original data set, and our analysis explains why this is the case. For the first time, these sample-then-scan algorithms allow spatial scan statistics to run on a million or more data points without making assumptions on the spatial distribution of the data. Moreover, our experiments and analysis give insight into when it is appropriate to trust the various types of spatial anomalies when the data is modeled as a random sample from a larger but unknown data set.