A noninformative Bayesian approach
Malay Ghosh, Glen D. Meeden · 2021
In many areas of statistics it is possible to give a noninformative Bayesian justification for standard frequentist methods. This chapter summarizes the Bayesian and predictive approach to finite population sampling and noted that in this approach the design probabilities play no role in the final analysis. It demonstrates the stepwise Bayes technique, and proves the admissibility of the maximum likelihood estimator in a binomial problem. The chapter describes a complete class theorem for problems with a finite sample space and finite parameter space. It explains the admissibility of the sample mean when estimating the population mean in a finite population sampling problem. The chapter shows how the stepwise Bayes technique can yield admissible set estimation procedures for certain problems in finite population sampling. It recalls some facts about the Polya urn distribution, and shows how point and set estimators based on the Polya posterior can be found approximately in practice.