Uniqueness condition for an auto-logistic model

Auto-logistic models are widely used to describe binary images texture and spatial presence–absence data. There exist some techniques, like Gibbs sampler algorithm among others, that allow simulating the process, but its performance depends on the model global properties at Z2. Under general conditions there will be at least a global distribution which conditionals are Gibbs specifications. The present work establishes sufficient conditions on the parameters of an auto-logistic model, in order to ensure the distribution’s uniqueness.