Bayesian Analysis of Binary Data Subject to Misclassification

This paper considers estimation of success probabilities of categorical binary data subject to misclassification errors from the Bayesian point of view. It has been shown by Bross (1954) that sample proportions are in general biased estimates. This bias is a function of the amount of misclassification and can be substantial. Tenenbein (1970) proposed to eliminate the bias by subjecting a portion of the sample to both true and fallible classifiers, resulting in a 2 x 2 table, from which the misclassification rates can be estimated. The rationale is that fallible classifiers are inexpensive relative to infallible ones. Hence if only a part of the sample is measured by the infallible classifier one can obtain a more efficient estimate, for a given sampling budget, than by measuring the whole sample using the infallible classifier. In many contexts an infallible classifier is unavailable or prohibitively expensive. Bayesian methods then provide a useful approach for dealing with the conseq..