More efficient inferences using ranking information obtained from judgment sampling

Judgment poststratification is an extension of ranked set sampling. It arises when sampled units from a population can be ranked rather easily without actually measuring the variable of interest and when determining the actual values can be expensive and time consuming. Under such a scheme, samples will contain units for which the variable of interest is observed while for others only that they are larger or smaller than one of the observed units. This paper will argue that standard methods ignore information contained in such samples and show that an objective step-wise Bayes analysis based on the Polya posterior leads to improved inferential procedures.