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In this paper we propose a prior distribution for the clique set anddependence structure of binary Markov random fields (MRFs). In the formulationwe allow both pairwise and higher order interactions. We construct the prior byfirst defining a prior for the neighbourhood system of the MRF, and conditionedon this we define a prior for the appearance of higher order interactions.Finally, for the parameter values we adopt a prior that allows for parametervalues to equal, and in this way we reduce the effective number of freeparameters. To sample from a resulting posterior distribution conditioned on anobserved scene we construct a reversible jump Markov chain Monte Carlo (RJMCMC)algorithm. We circumvent evaluations of the intractable normalising constant ofthe MRF when running this algorithm by adopting a previously definedapproximate auxiliary variable algorithm. We demonstrate the usefulness of ourprior in two simulation examples and one real data example.

Prior specification of neighbourhood and interaction structure in binary Markov random fields