Density Estimation of Spatio-temporal Point Patterns Using Moran's Statistic

Abstract

Moran's Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of the disease spread over time, steered by a common factor in the scale. The main consequence of our results is that our Moran statistic is calculated from an explicit algorithm in a Monte Carlo simulation setting. Results are compared to Geary's statistic and estimates of parameters under Poisson process are given.