Comments on 'A theoretical analysis of Monte Carlo algorithms for the simulation of Gibbs random field images'

Contrar y to the conclus ions of the paper by J. K. Goutsias, the relative entropy of the initial distribulion for a Monte Carlo simu­ lation is not monotonicall y related to the degree of convergence after some given number of steps, and optimal single -step convergence is not achieved by the Gibbs sampler with systematic site ordering. Some aspects of this work could nevertheless be useful. Index Terms-Monte Carl o simulation, Gibbs sampling, relative en­ tropy_ In the above paper,l J. K. Goutsias presents an analysis of Monte Carlo sampling methods based on Markov chains, such as are employed in image processing applications. Unfortunately, while some of his results are interesting, not all of them are entirely correct. In his analysis, Goutsias measures the distance between the distri­ bution produced at step m of the Markov chain, p( m) , and the desired stationary distribution, rr, by the "relative entropy", D(rrllp(m)) =