An approach to hypothesis testing based on local indicators of spatio-temporal association

The detection of clustering structure in a point pattern is one of the major focus of attention in spatio-temporal data mining. For instance, statistical tools for clustering detection and identification of events belonging to clusters are welcome in epidemiology and seismology. Local second-order statistics can provide information on how an event relates to nearby events. We extend local indicators of spatial association (known as LISA functions) into the spatio-temporal context (which then will be called LISTA functions). These functions can be used for local tests in the context of case-control spatio-temporal point patterns, and are able to assess in the neighbourhood of each event if the two point patterns have a different structure. We present a simulation study and apply this methodology to earthquakes data