Methods for Monitoring of Spatial Patterns
Peter Rogerson Principal Investigator
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Spatial pattern detection is routinely carried out in fields such as criminology and epidemiology, where the usual motivation is to find clusters of events. The techniques employed are retrospective, in the sense that a map of previous events such as crimes or diseases is examined for evidence of clustering. This project will extend methods of spatial pattern detection by developing extensions to the case of monitoring new point events as they are received over time. In particular, current statistical tests for spatial pattern detection will be combined with the cumulative sum methods used by industry in quality control applications. The cumulative sum methods employed will include multivariate approaches, where regional counts of events may be summarized in a multivariate vector. The effectiveness of alternative methods will be assessed using simulated data series for which the true nature of the changes in geographic patterns is known. The new methods are designed with the objective of quick detection in mind and they will allow point patterns to be monitored for changes in real time.<br/><br/>There are many situations where a two-dimensional pattern of points gives rise to the question of whether a pattern is present. Criminologists are interested in patterns of crime, epidemiologists are interested in patterns of disease, market researchers are interested in the locations of their customers, and engineers are interested in the locations of defects that occur in the fabrication of integrated circuits. Methods of pattern detection are currently used retrospectively by carrying out a statistical test at a single point in time. However, many applications are better suited to repeated tests, so that changes in pattern may be monitored, as data on new locations becomes available. This project will include (a) the development of new methods that combine current approaches to pattern detection with the monitoring methods used in industrial quality control, and (b) application of the new methods to problems in epidemiology and criminology.