Bayesian inference of a binomial proportion using one-sample misclassified binary data

Misclassified binary data result from using a fallible classifier for classifying units into two categories. If an infallible classifier is also available, a random subsample of this misclassified data can be further classified using the infallible classifier. For such data, the existing methods for exact confidence interval are too conservative, and the existing Bayesian credible interval suffers from computational difficulty. We derive a closed-form Bayesian algorithm which draws a posterior sample of the proportion parameter from the exact marginal posterior distribution. Our simulations show that our Bayesian algorithm is easy to implement and has nominal coverage.