Fully Bayesian binary Markov random field models: Prior specification and posterior simulation

摘要

We propose a flexible prior model for the parameters of binary Markov randomfields (MRF) defined on rectangular lattices and with maximal cliques definedfrom a template maximal clique. The prior model allows higher-orderinteractions to be included. We also define a reversible jump Markov chainMonte Carlo (RJMCMC) algorithm to sample from the associated posteriordistribution. The number of possible parameters for an MRF with for instance kx l maximal cliques becomes high even for small values of k and l. To get aflexible model which may adapt to the structure of a particular observed imagewe do not put any absolute restrictions on the parametrisation. Instead wedefine a parametric form for the MRF where the parameters have interpretationas potentials for the various clique configurations, and limit the effectivenumber of parameters by assigning apriori discrete probabilities for eventswhere groups of parameter values are equal. To run our RJMCMC algorithm we haveto cope with the computationally intractable normalising constant of MRFs. Forthis we adopt a previously defined approximation for binary MRFs, but we alsobriefly discuss other alternatives. We demonstrate the flexibility of our priorformulation with simulated and real data examples.