An efficient estimator for the expectation ∫f\dP is constructed, where P is a Gibbs random field, and f is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer \cite{greenwood_wefelmeyer_1999}, and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.
A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs-Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood (MPL) estimate, or directly by Möbius formula.