C enter for S tatistical E cology and E nvironmental S tatistics PULSE , Progressive Upper Level Set Scan Statistic for Geospatial Hotspot Detection

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the agencies. 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. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the agencies. 1 1. Introduction A scan statistic is commonly used in geospatial hotspot detection. A geospatial region is tessellated into 'cells'. Data from the region in the form of responses from individual cells are available. One is interested in identifying a cellular zone, if one exists, with unusually elevated response compared with the rest of the cells. Such a zone is called a hotspot. Following the pioneering work of Joseph Naus and his students on the scan statistic, " the literature on the scan statistic is … growing exponentially in diverse directions, with contributions by many researchers and groups. …