The problem of space-time cluster detection arises in a variety of applications, including disease surveillance and brain imaging. In this work, we briefly review the state of the art in space-time cluster detection, focusing on space-time scan statistics, and we derive a number of new statistics. First, we distinguish between tests for clusters with higher disease rates inside the cluster than outside (as in the traditional spatial scan statistics framework) and tests for clusters with higher counts than expected (as is appropriate when inferring the expected counts in a region from the time series of past counts). Second, we distinguish between tests for "persistent" clusters (where the disease rate remains constant throughout the duration of a cluster) and tests for "emerging" clusters (where the disease rate increases monotonically through the duration of a cluster). These new statistics for spatio-temporal cluster detection will serve as the basis for our future work in detection of emerging space-time clusters.

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