Coverage Probability of the Credible Interval and Credible Probability of the Confidence Interval of the Hierarchical Normal Model

It is well known that the coverage probability of a given nominal level confidence interval and the credible probability of a given nominal level credible interval will attain the nominal level. Moreover, it is commonly believed that the two switching concepts probabilities, that is, the coverage probability of a given nominal level credible interval and the credible probability of a given nominal level confidence interval, can not attain the nominal level in general. For the hierarchical normal model, we show that the two switching concepts probabilities can attain the nominal level in the limit when a skillful classified variable is infinity. The numerical simulations illustrate the correctness of our findings.