The accuracy of Gibbs sampling, a Markov chain Monte Carlo procedure, was considered for estimation of item and ability parameters under the two-parameter logistic model. Memory test data were analyzed to illustrate the Gibbs sampling procedure. Simulated data sets were analyzed using Gibbs sampling and the marginal Bayesian method. The marginal Bayesian method combined with the expected a posteriori estimation of ability yielded consistently smaller root mean square errors and better bias results than Gibbs sampling. (Contains 12 figures, 29 tables, and 56 references.) (Author)