PULSE, progressive upper level set scan statistic for geospatial hotspot detection

Abstract

This paper presents a scan statistic, progressive upper level set (PULSE) scan statistic, for geospatial hotspot detection and its software implementation. Like ULS, the PULSE scan statistic is based on the arbitrarily shaped scan window and can be adapted for a network setting. PULSE is a refinement of the upper level set (ULS) scan statistic. Like some other likelihood based scanning devices, the ULS scan statistic identifies maximum likelihood estimate (MLE) zones that tend to be ‘stringy’ and sprawling. Its search path increases possibility of inclusion of extraneous cells in its MLE zones and, to a smaller extent, of exclusion of cells that belong to a true hotspot from its MLE zone. The PULSE scan statistic achieves improvement over the ULS scan statistic in two ways. First, it begins its search for a most likely zone with a large population of candidate zones obtained by modifying the ULS tree structure and continues its search using a genetic algorithm. Secondly, to reduce chances of generating an MLE that is excessively stringy and that includes extraneous cells in the MLE zone, PULSE uses cardinality and compactness of zones along with their likelihoods as the fitness function in the genetic algorithm and uses several pertinent criteria including evenness of intra-zone cellular response ratios to determine the MLE zone. To reduce computation, Gumbel distribution of extreme values is used to determine the p-value of the MLE zone. Better results come at the cost of increased processing time. An evaluative performance study is presented.