Doctor of Philosophy
Statistics and Actuarial Sciences
Dr. Charmaine Dean and Dr. W. John Braun
In biostatistics and environmetrics, interest often centres around the development of models and methods for making inference on observed point patterns assumed to be generated by latent spatial or spatio-temporal processes. Such analyses, however, are challenging as these data are typically hierarchical with complex correlation structures. In instances where data are spatially aggregated by reporting region and rates are low, further complications may result from zero-inflation.
In this research, motivated by the analysis of spatio-temporal storm cell data, we generalize the Neyman-Scott parent-child process to account for hierarchical clustering. This is accomplished by allowing the parents to follow a log-Gaussian Cox process thereby incorporating correlation and facilitating inference at all levels of the hierarchy. A primary focus for these data is to jointly model storm cell detection and trajectories. To do so, storm cell duration, speed and direction are included in a marked point process framework. The thesis also proposes a general approach for the joint modelling of multivariate spatially aggregated point processes with the observed outcomes being zero-inflated count random variables. For such models, we incorporate correlation between the random field assumed to generate events and mean event counts. This is applied to lung and bronchus cancer incidence by public health unit in Ontario and a study of Comandra blister rust infection of lodgepole pine trees in British Columbia.
The key contributions from this thesis include the following: 1) developing a spatio-temporal hierarchical cluster process that incorporates correlation at all levels of the hierarchy, 2) joint modelling of a hierarchical cluster process and multivariate marks, 3) extending the framework for the joint modelling of multivariate lattice data to enable decomposition of the sources of shared spatial structure and 4) investigating aspects of the partial misspecification of joint spatial structure for multivariate lattice data.
Albert-Green, Alisha, "Joint Models for Spatial and Spatio-Temporal Point Processes" (2016). Electronic Thesis and Dissertation Repository. 4306.