A Bayesian Approach to Some Best Population Problems

Abstract : Certain best population problems adopting a Bayesian approach were investigated. One main advantage of such an approach is that satisfactory decision procedures can be obtained in the presence of nuisance parameters. The use of Bayes' theorem allows one to analyze best population problems from many points of view. A general description of best population problems is outlined. The criterion for 'bestness' is regarded as a 'utility' function of the statistician. The decision procedure then adopted is based upon the principle of maximizing posterior expected utility. The application of this procedure when sampling from normal populations and exponential populations was discussed. The criterion defining the best population is taken to be the coverage of the population considered in a certain given interval. The procedures are shown to be consistent. The decision analysis by considering the pos terior distribution of the criterion is presented. This extension enables other decision procedures to be proposed which may be more appropriate in certain situations than that resulting from the principle of maximizing posterior expected utility.