In Meeden and Ghosh (1983) a theory was developed for choosing, possibly at random, from a group of experiments the one to be observed. Here we consider the problem when the class of possible designs is restricted to a subclass of all designs. A theorem which identifies some admissible decision procedures and generalizes the early work is proved. Some applications to finite population sampling are discussed.
"Using the Stepwise Bayes Technique to Choose Between Experiments." Ann. Statist. 15 (1) 269 - 277, March, 1987. https://doi.org/10.1214/aos/1176350265