Abstract
In this paper, we consider spatial point processes and investigate members of a subclass of the Markov point processes, termed the directed Markov point processes (DMPPs), whose joint distribution can be written in closed form and, as a consequence, its parameters can be estimated directly. Furthermore, we show how the DMPPs can be simulated rapidly using a one-pass algorithm. A subclass of Markov random fields on a finite lattice, called partially ordered Markov models (POMMs), has analogous structure to that of DMPPs. In this paper, we show that DMPPs are the limits of auto-Poisson and auto-logistic POMMs. These and other results reveal a close link between inference and simulation for DMPPs and POMMs.
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Cressie, N., Zhu, J., Baddeley, A.J. et al. Directed Markov Point Processes as Limits of Partially Ordered Markov Models. Methodology and Computing in Applied Probability 2, 5–21 (2000). https://doi.org/10.1023/A:1010095300231
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DOI: https://doi.org/10.1023/A:1010095300231