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

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Abstract

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.

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  1. Petter Arnesen

    Present address: Department of Transport Research, Sintef, Trondheim, Norway

Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Petter Arnesen & Håkon Tjelmeland

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  1. Petter Arnesen
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  2. Håkon Tjelmeland
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Correspondence to Håkon Tjelmeland.

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Arnesen, P., Tjelmeland, H. Prior specification of neighbourhood and interaction structure in binary Markov random fields. Stat Comput 27, 737–756 (2017). https://doi.org/10.1007/s11222-016-9650-5

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