Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider a two-stage cluster sampling design where the clusters are first selected with probability proportional to…

To test the use of Bayes's theorem to adjust for nonresponse bias, 600 hospitals were used in a simulated sample survey. On the basis of known information on five variables, Bayes's formula correctly predicted the status of 92 of the 100 "nonrespondents" relative to a sixth variable. (Author/BW)