Analysing spatio-temporal autocorrelation with LISTA-viz

Many interesting analysis problems (e.g. disease surveillance) would become more tractable if their spatio-temporal structure was better understood. Specifically, it would be helpful to be able to identify autocorrelation in space and time simultaneously. Some of the most commonly used measures of spatial association are LISA statistics, such as the Local Moran's I or the Getis-Ord Gi*; however, these have not been applied to the spatio-temporal case (including many time steps) because of computational limitations. We have implemented a spatio-temporal version of the Local Moran's I and claimed two advances: first, we exploit the fact that there are a limited number of topological relationships present in the data to make Monte Carlo's estimation of probability densities computationally practical, and thereby bypass the 'curse of dimensionality'. We term this approach 'spatial memoization'. Second, we developed a tool (LISTA-Viz) for interacting with the spatio-temporal structure uncovered by the statistics that contains a novel coordination strategy. The potential usefulness of the method and the associated tool are illustrated by an analysis of the 2009 H1N1 pandemic, with the finding that there was a critical spatio-temporal 'inflection point' at which the pandemic changed its character in the United States.