The ability estimates of Gibbs sampling and the magnitudes of the posterior standard deviations were investigated. Item parameters of the Q-E intelligence test (J. Fraenkel and N. Wallen, 2000) for 44 examinees were obtained using Gibbs sampling, marginal Bayesian estimation, and BILOG. Two normal priors were used in item parameter estimation. Ability estimates were obtained using Gibbs sampling, that is, jointly with item parameter estimates, and compared with estimates from the expected a posteriori method using item parameter estimates obtained from Gibbs sampling, marginal Bayesian estimation, and BILOG. Item parameter estimates were very similar, as were ability estimates, but the patterns of the magnitudes of the posterior standard deviations of ability estimates from Gibbs sampling were different from those based on the expected a posteriori method. (Contains 7 tables, 4 figures, and 45 references.) (Author/SLD)