Spatial Point process are often modeled as Markov fields, and inference for such models are sometimes either inefficient or computationally intensive due to difficulties in evaluating the normalizing constant. Simulation study for such process is hard. We exploit the partial order in the plane and introduce a class of Markov point processes known as "Directed Markov Point Processes" and investigate their properties. This Markov structure enables to study some of the well known spatial processes in detail. Conditional intensity plays an important role in determining the distribution of such processes. We explore how the notion of random spatial change, well known in the area of stochastic process, provides a tool to simulate directed Markov point processes using conditional intensity.
This is a joint work with Adrian Baddeley (The University of Western Australia) and Noel Cressie (The Ohio State University).