Frequentist Bayesian compound inference

In practice often either the Bayesian or frequentist method is used, although there are some combined uses of the two methods, a formal unified methodology of the two hasn’t been seen. Here we first give a brief review of the two methods and some combination of the two, then propose a procedure using both the frequentist likelihood and the Bayesian posterior loss in parameter estimation and hypothesis testing, as an attempt to unify the two methods. Basic properties of the proposed method are studied, and simulation studies are carried out to evaluate the performance of the method.