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Interval estimation for the proportion parameter in one-sample misclassified binary data has caught much interest in the literature. Recently, an approximate Bayesian approach has been proposed. This approach is simpler to implement and performs better than existing frequentist approaches. However, because a normal approximation to the marginal posterior density was used in the Bayesian approach, some efficiency may be lost. We develop a closed-form fully Bayesian algorithm which draws a posterior sample of the proportion parameter from the exact marginal posterior distribution. We conducted simulations to show that our fully Bayesian algorithm is easier to implement and has better coverage than the approximate Bayesian approach.

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