Statistics and Computing

, Volume 27, Issue 3, pp 737–756 | Cite as

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

  • Petter Arnesen
  • Håkon TjelmelandEmail author


We formulate a prior distribution for the energy function of stationary binary Markov random fields (MRFs) defined on a rectangular lattice. In the prior we assign distributions to all parts of the energy function. In particular we define priors for the neighbourhood structure of the MRF, what interactions to include in the model, and for potential values. We define a reversible jump Markov chain Monte Carlo (RJMCMC) procedure to simulate from the corresponding posterior distribution when conditioned to an observed scene. Thereby we are able to learn both the neighbourhood structure and the parametric form of the MRF from the observed scene. We circumvent evaluations of the intractable normalising constant of the MRF when running the RJMCMC algorithm by adopting a previously defined approximate auxiliary variable algorithm. We demonstrate the usefulness of our prior in two simulation examples and one real data example.


Auxiliary variables Fully Bayesian model Ising model Markov random fields Reversible jump MCMC 

Supplementary material

11222_2016_9650_MOESM1_ESM.pdf (429 kb)
Supplementary material 1 (pdf 428 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of Transport ResearchSintefTrondheimNorway

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