A simple algorithm for delta method variances for multinomial posterior bayes probability estimates

Abstract

The uncertainty in the estimated posterior multinomial probabilities which results from applying Bayes rule using conditional probabilities estimated from a limited data base is investigated. The first order Taylor series estimator for the variance of the estimated posterior probabilities was developed. A simulation study was conducted to ascertain the accuracy of these approximate variance estimates. In addition, the accuracy of both posterior probability estimates and the variance estimates is evaluated for data bases of various sizes. The method is appropriate for any of the usual medical diagnostic problems in which Bayesian methods are applied

Keywords:

• Bayes probability
• diagnostic test
• delta method