Bayes Sequential Designs of Fixed Size Samples from Finite Populations

The problem of choosing a sample of a fixed size from a finite population is studied in the framework of Bayes designs. The conjectured non-randomized character of Bayes designs is verified. Bayes designs are shown to be without replacement selections, which are generally sequential ones. Sufficient conditions are provided for the optimality of single-phase designs. An example is provided of a case in which the optimal Bayes design is sequential.