Detecting space-time anomalies in point process models of intelligent site selection

The main goal of this research is to generate a methodological framework for the statistical detection of change in an intelligent site selection (ISS) process. An ISS process is one in which an actor judiciously selects the location and time to initiate an event according to their preferences or perceived utility of that location and time. A fundamental difference between an ISS process and other space-time point processes is its dependence on the realization of some external covariate processes.; A methodological framework is established for the statistical detection of anomalies between two spatial ISS point processes. The two processes could represent two time periods or two types of events such as case-control. By modeling the locations of events in each process as a marked point process, we can then detect differences in the intensity of each component process. A modified PRIM (patient rule induction method) is implemented to partition the high dimensional feature space, which can include mixed variables, into the most likely change regions. Monte Carlo simulations are easily and quickly generated under random relabeling to test a scan statistic for significance. By detecting local regions of change, not only can it be determined if change has occurred in the study area, but the specific region where change occurs is also identified.; Next, consideration of ISS anomaly detection is expanded to the surveillance problem. Instead of fixing the time period to test for change, we now perform sequential analysis to quickly detect when an anomaly occurs and the corresponding change region. Difficulties arise for several reasons: the high-dimensional complex ISS models are of an unknown form or have unknown parameters both pre and post change, the anomalous region is unknown, the time of the change is unknown, and multiple hypothesis testing problems will result from both searching over all possible change regions and change times. A likelihood based methodology is developed that addresses these difficulties. This method expands on some common change detection methods (such as CUSUM, SR, and GLR) while maintaining their simplicity and recursive computation even under multiple unknown parameters. We discuss the derivation of our procedure along with several properties of our methodology related to standard change detection criteria.