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

Article type: Research Article

Authors: Rahardja, Dewi^{; *} | Zhao, Yan D.

Affiliations: Department of Clinical Sciences and Simmons Cancer Center, University of Texas Southwestern Medical Center, Dallas, TX, USA

Correspondence: [*] Corresponding author. E-mail: rahardja@gmail.com.

Abstract: 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.

Keywords: Bayesian credible interval, Binary data, Double sampling, Misclassification, Proportion

DOI: 10.3233/MAS-2011-0197

Journal: Model Assisted Statistics and Applications, vol. 7, no. 1, pp. 17-22, 2012