A simulation-based estimator for hidden Markov random fields

An estimator for estimating the parameters of a Markov random field X from inaccurate observations is introduced. The author considers first a Markov (Gibbs) random field X={X_i,j} on a lattice L={(i ,j): i=1,2,. . .,n; j=1,2,. . .,m}. The marginal distributions of (X_i,j, X_i+u,j+v) (u,v=-1,0,1) are first estimated from an image. Then, random fields X* are simulated with the probability of X*_i+u,j+v)=b nearly equal to the estimate of P{X_i,j=X _i+u,=b}. A simulation method similar to the Gibbs sampler is used. The parameters of the Markov random field model are estimated from the X*´s with the pseudolikelihood method