Estimating the Granularity Coefficient of a Potts-Markov Random Field within a Markov Chain Monte Carlo Algorithm

This paper addresses the problem of estimating the Potts parameter beta jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on beta requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method, the estimation of beta is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating beta jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of beta. On the other hand, choosing an incorrect value of beta can degrade estimation performance significantly. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images.