Interval estimation of binomial proportions based on weighted Polya posterior

Abstract

Recently the interval estimation of binomial proportions is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the well-known Wald confidence interval. Various alternatives have been proposed. Among them, Agresti–Coull confidence interval has been recommended by Brown et al. [2001. Interval estimation for a binomial proportion. Statist. Sci. 16, 101–133] with other confidence intervals such as the Wilson interval and the equal tailed interval resulting from the natural noninformative Jefferys prior for a binomial proportion. However, it seems that Agresti–Coull interval is little bit wider than necessary when sample size is small, say n ⩽ 40 . In this note, an interval estimator is developed using weighted Polya posterior. It is shown that the confidence interval based on the weighted Polya posterior is essentially the Agresti–Coull interval with some improved features.