An Introduction to Spatial Point Processes and Markov Random Fields

Binary-valued Markov random fields may be used as models for point processes with interactions (e.g. repulsion or attraction) between their points. This paper aims to provide a simple nontechnical introduction to Markov random fields in this context. The underlying spaces on which points occur are taken to be countable (e.g. lattice vertices) or continuous (Euclidean space). The role of Markov random fields as equilibrium processes for the temporal evolution of spatial processes is also discussed and various applications and examples are given.

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