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Abstract:
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The need to model spatial fields of binary variables arises in numerous contexts, including monitoring for the presence/absence of animal species or other events in ecological and environmental studies. Markov random field models have frequently been used in these situations, and the notion that variables closer together in space should be more similar that those farther apart results in a common assumption that spatial dependencies will be positive. Negative spatial dependencies are theoretically possible in Markov random field models, but their interpretation can be difficult or even intuitively impossible for certain neighborhood structures (e.g., classic 8 nearest neighbors on a regular lattice). Nevertheless, simulations of random fields using models with negative dependencies exhibit interesting structures. We consider the use of several simple diagnostics to quantify these patterns, and explore issues that arise through the interaction of dependencies and neighborhood specifications.
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