Polya Posterior Quantile Estimation for Stratified Populations

We develop extensions of the Polya posterior that can be used to estimate population quantiles in stratified populations. In the simple case with no auxiliary information, estimates based on this extension to the Polya posterior perform similarly to the standard frequentist estimates. The Polya posterior can be extended to incorporate a variety of prior knowledge about an auxiliary characteristic. In particular, we consider estimation of population quantiles for stratified populations when there exists prior knowledge that a population quantile of an auxiliary variable lies in a specified interval. This type of prior information is difficult to exploit using standard methods. We show how a constrained version of the Polya posterior can use this information to obtain improved point and interval estimators of a population quantile.