Directed Markov Point Processes as Limits of Partially Ordered Markov Models

Noel Cressie (), Jun Zhu (), Adrian J. Baddeley () and M. Gopalan Nair ()
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Noel Cressie: The Ohio State University
Jun Zhu: Iowa State University
Adrian J. Baddeley: The University of Western Australia
M. Gopalan Nair: Curtin University of Technology

Methodology and Computing in Applied Probability, 2000, vol. 2, issue 1, 5-21

Abstract: 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.

Keywords: directed pairwise-interaction point process; directed Strauss process; Markov random field; simulation; spatial point process (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1010095300231

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