Beta-binomial model, which is reparametrized in terms of the mean probability $mu$ of a positive deagnosis and the $kappa$ of agreement, is widely used in psychology. When $mu$ is close to 0, inference about $kappa$ become difficult because likelihood function becomes constant. We consider Bayesian approach in this case. To apply Bayesian analysis, Gibbs sampler is used to overcome difficulties in integration. Marginal posterior density functions are estimated and Bayesian estimates are derived by using Gibbs sampler and compare the results with the one obtained by using numerical integration.