A multivariate spatial point process model: Theory, simulation, and application

Markov point processes provide flexible models to describe interaction behavior amongst points, including points of different types. However, simulation and estimation for Markov point processes are often challenging due to the computational and mathematical complexity needed to obtain desired solutions. In this dissertation, we propose and study in depth a multi-type Markov point process model to seek a balance between the capability to model interactions and the complexity of simulation and estimation. The model only formulates explicitly interaction patterns between points of different types; interactions between points of the same type, on the other hand, arise implicitly. The behaviors of the proposed multi-type Markov process model is explored in depth. This dissertation investigates the performance of the Gibbs sampler relating to the model, the behavior of the process in regards to various spatial process summary statistics, the performance and convergence properties of pseudo-likelihood based inference, and the application of the model in regards to plant species data.