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We consider statistical inference from incomplete sets of binary data. Our approach is based on the autologistic model, which is very flexible and well suited for medical applications. We propose a Bayesian approach, essentially using Monte Carlo techniques. The method developed in this paper is a special version of Gibbs sampler. We repeat intermittently the following two steps. First, missing values are generated from the predictive distribution. Second, unknown parametes are estimated from the completed data. The Monte Carlo method of computing maximum likelihood estimates due to Geyer and Thompson (J. R. Statist. Soc. B 54: 657-699, 1992) is modified to the Bayesian setting and missing data problems. We include results of some small scale simulation experiments. We artificially introduce missing values in a real data set and then use our algorithm to refill missings. The rate of correct imputations is quite satisfactory. [ABSTRACT FROM AUTHOR]