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

Nicholas Malizia

doi:10.1371/journal.pone.0052034

Abstract

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.

Highlights

The space-time permutation scan statistic, introduced by [1], is used to identify clusters, or hotspots, of space-time interaction within patterns of spatio-temporal events
The spatial and temporal perspectives of these results show that for the majority of the perturbed patterns, the space-time permutation scan statistic (STPSS) identified Cluster 1 as the most likely cluster (MLC) in spite of the perturbations; Cluster 2 was frequently identified as the MLC even though it was seeded with less events, having a larger initial pvalue and a smaller likelihood of being identified as the MLC in the original data
These results suggest that with decreased spatial accuracy, the STPSS may be less likely to pick out the true MLC amongst other possible clusters

Summary

Introduction

The space-time permutation scan statistic, introduced by [1], is used to identify clusters, or hotspots, of space-time interaction within patterns of spatio-temporal events. The expected number of cases in each area and time period (i.e. mst) is calculated by conditioning on the observed marginals as shown in Equation 2. The STPSS assumes the function responsible for the generation of events operates uniformly across all time periods and areal subdivisions [1]. This is in contrast to other similar methods such as the cylindrical and flexibly shaped space-time scan statistics which assume spatial and temporal heterogeneity in the data generating process

Methods

Results

Conclusion