Bayesian confidence intervals of proportion with misclassified binary data?

A Bayesian approach is considered for the interval estimation of a binomial proportion in doubly sampled data. The coverage probability and the expected width of the Bayesian confidence interval are compared with likelihood-related confidence intervals. It is shown that a hierarchical Bayesian approach provides relatively simple and effective confidence intervals. In addition, it is shown that Agresti-Coull type confidence interval, discussed by Lee and Choi (2009), can be justified by the Bayesian framework.