Spatial Point Pattern Analysis Using Composite Likelihood

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The proposed research introduces a new likelihood based method in fitting spatial point process models using the idea of composite likelihood. Composite likelihood (CL) has been successfully applied in numerous settings where a full maximum likelihood is not feasible or is not available. Its use in spatial point process modeling, however, has never been studied. This research intends to show that a CL can be formed for any spatial point process whose second-order intensity function can be explicitly defined. The proposed likelihood is easy to obtain and can be used in many different spatial point pattern analyses. In particular, it can be used to fit both homogeneous and inhomogeneous spatial point process models to data. Furthermore, it can also be used to select the bandwidth used in estimating the pair correlation function, which is an extremely exploratory and model fitting tool in spatial point pattern analysis.This research is motivated by the red oak borer data that were collected by entomologists at the University of Arkansas. The data consist of mapped locations of attack holes caused by larvae of red oak borers when they eat their way into the trees. The main objective is to understand what affects adult red oak borers to decide where to lay their eggs. The proposed model fitting procedures will be applied to link the locations of attack holes to important tree characteristics such as side and height of the tree. This work will have both important biological and practical significance. In particular, the results will provide biological insight on the breeding habit of the adult borers. This biological insight can in turn be used in practice to guide the development of more effective trapping techniques that can be used to control the population of the red oak borers. Thus the proposed research may play a critical role in the effort to save millions of red oak trees in the US that are being threatened by the outbreaks of red oak borers.