Reconstructing point patterns from spatially aggregated data

Abstract

In this thesis we explore the ability to reconstruct samples (point configurations) from a point process, based only on the information contained in spatially aggregated data, namely the number of points in the partitions of a larger region. The ability to reconstruct a point configuration, in such a way that it retains most of it’s statistical properties, could be useful in cases where one is faced with a mixed dataset; some regions containing the full point configuration data, while other regions only contain aggregated data, i.e. the counts of subregions. Our main motivation in this thesis however, concerns epidemic modelling, where the locations of individual infections are represented by point(-configuration)s, drawn from a hypothetical point process model, and typically, data is only available in spatially aggregated form. Here we present a scheme for reconstructing point configurations, as well as a collection of dissimilarity measures to assess the quality of reproduction. These are then analysed (in part) theoretically and verified using simulation studies. We obtain constraints regarding the size of the partitions/subregions in order for the reconstructed point configuration to retain important statistical properties of the original point process.