  This report considers the problem of computing the Cramer-Rao bound for the
parameters of a Markov random field. Computation of the exact bound is not
feasible for most fields of interest because their likelihoods are intractable
and have intractable derivatives. We show here how it is possible to formulate
the computation of the bound as a statistical inference problem that can be
solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo
method. The proposed methodology is successfully applied on the Ising and the
Potts models.% where it is used to assess the performance of three state-of-the
art estimators of the parameter of these Markov random fields.
