A Posterior Density for the Difference Between Two Binominal Proportions and the Highest Posterior Density Credible Interval

Abstract

The statistical inference concerning the difference between two independent binominal proportions has often been discussed in medical and statistical literature. This discussion is far more often based on the frequency theory of statistical inference than on the Bayesian theory. In this article, we propose the expression of the posterior probability density function (pdf) for the difference between two independent binominal proportions. In addition, we calculate the exact Highest Posterior Density (HPD) credible interval by using this expression. We also compare both the exact HPD credible interval and the approximate credible interval. We find that the former always has a narrower interval length than the latter.