A Simulated Annealing Strategy for Cluster Detection

We discuss and implement a new strategy for spatial cluster detection. A test statistic based on the likelihood ratio is used, as formulated by Kulldorff and Nagarwalla. Differently from these authors, our test is not restricted to the detection of clusters with fixed shape, such as rectangular or circular shape, but it looks for connected clusters with arbitrary geometry. This could be advantageous in real situations, where we frequently find spatial clusters along rivers or transport ways, for example. A new technique of adaptive simulated annealing is developed, focused on the problem of finding the local maxima of a certain likelihood function over the space of the connected subgraphs of the graph associated to the map of populations and geo-referenced cases. This algorithm has applications to the study of disease clusters and hot-spots of criminality. We present a study case for homicides in the city of Belo Horizonte, Brazil.