We investigate the problem of estimating the ratio of subjects that share a particular characteristic in a population, but some degree of misclassification is possible. The misclassification probabilities are considered as the random variables, and we study a Bayesian approach to this problem. We propose a method to calculate the exact posterior density of the ratio, based on some prior distributions. We, then, study a method to determine the sample size, using average coverage criterion. We also investigate the effect of different prior distributions on the sample size.

Keywords: Average Coverage Criterion, Bayes Estimator, Binomial Distribution, Misclassification, Sample Size

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