Analysis of point patterns of events is an important aspect in the literature of spatial statistics. In this thesis, we are interested in point patterns of events that occur in a network of lines, such as street crimes mapped on a road network. Applying standard statistical techniques designed to analyse point patterns in two-dimensional space, such as use of the Ripley's K function, does not take into account the constraint that spatial points can only occur on the line segments of the network. It was not until the work of Okabe and Yamada that relevant methods were used to analyse point patterns in a network. They proposed a 'network K function', which takes into consideration the geometrical properties of the network. However, interpretation of the network K function is difficult, because its values depend on the geometry of the network. Here, we develop new methods and theory for analysis of point patterns in a linear network and propose a reweighted K function that intrinsically compensates for the geometry of the network to overcome these problems. The reweighted K function is an extension of Ripley's K function in that 'weights' are applied according to the structure of the network, and the Euclidean distance is replaced with the shortest path distance measured in the network. The newly proposed K function is further extended to the inhomogeneous case such that spatial inhomogeneity can be accounted for. We demonstrate the use of these K functions on an application to the ecology of urban wall spiders Oecobius annulipes Lucas.
|Publication status||Unpublished - 2010|