Directed Markov point processes as limits of partially ordered Markov models (Q1577406)

A certain class of spatial point processes, termed directed Markov point processes (DMPP's) is defined. DMPP's have the property that their joint distribution can be written in closed form. Thus its parameters can be estimated directly and they can be simulated rapidly. It is shown that DMPP's are the limits of auto-Poisson and auto-logistic partially ordered Markov models as defined by \textit{N. Cressie} and \textit{J. L. Davidson} [Comput. Stat. Data Anal. 29, No. 1, 1-26 (1998)], which are important graphical models used in the analysis of networks.