Inaccuracy, uncertainty and the space-time permutation scan statistic.

The space-time permutation scan statistic (STPSS) is designed to identify hot (and cool) spots of space-time interaction within patterns of spatio-temporal events. While the method has been adopted widely in practice, there has been little consideration of the effect inaccurate and/or incomplete input data may have on its results. Given the pervasiveness of inaccuracy, uncertainty and incompleteness within spatio-temporal datasets and the popularity of the method, this issue warrants further investigation. Here, a series of simulation experiments using both synthetic and real-world data are carried out to better understand how deficiencies in the spatial and temporal accuracy as well as the completeness of the input data may affect results of the STPSS. The findings, while specific to the parameters employed here, reveal a surprising robustness of the method's results in the face of these deficiencies. As expected, the experiments illustrate that greater degradation of input data quality leads to greater variability in the results. Additionally, they show that weaker signals of space-time interaction are those most affected by the introduced deficiencies. However, in stark contrast to previous investigations into the impact of these input data problems on global tests of space-time interaction, this local metric is revealed to be only minimally affected by the degree of inaccuracy and incompleteness introduced in these experiments.