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We study the problem of estimating the one-point specification probabilitiesin non-necessary finite discrete random fields from partially observedindependent samples. Our procedures are based on model selection byminimization of a penalized empirical criterion. The selected estimatorssatisfy sharp oracle inequalities in $L_2$-risk. We also obtain theoreticalresults on the slope heuristic for this problem, justifying the slope algorithmto calibrate the leading constant in the penalty. The practical performances ofour methods are investigated in two simulation studies. We illustrate theusefulness of our approach by applying the methods to a multi-unit neuronaldata from a rat hippocampus.

Sharp oracle inequalities and slope heuristic for specification probabilities estimation in discrete random fields