A Bayesian method for using mean constraints in finite population sampling

The Bayesian approach to estimation in finite population sampling uses a posterior distribution to relate the observed to the unobserved members of a population. We will discuss one such approach which uses the Polya posterior as an objective predictive distribution for unobserved members conditional on sampled members. This posterior is a stepwise Bayes procedure which produces admissible point estimators of population parameter functions. We will show how certain kinds of information regarding the population mean can be combined with the Polya posterior to form a weighted Polya posterior. This modified posterior produces admissible estimators of the population mean which often perform better than standard finite population estimators. In Chapter 2 we will assume there exists a known lower bound for the population mean and in Chapter 3 we will assume there exists knowledge of an ordering between two population means. In the latter case, a joint weighted Polya posterior will be formed to estimate both population means and the difference between population means. We will demonstrate how the weighted posteriors from Chapters 2 and 3 can be used with annual Forest Inventory and Analysis data from the state of Indiana.