Bayesian multiple mean comparisons between two normal populations

The Bayesian multiple testing problem requires an examination of all conceivable configurations of true and false null hypotheses, a task that becomes increasingly intricate as the number of hypotheses increases. To tackle this issue, we propose an objective Bayesian multiple testing procedure aimed at facilitating mean comparisons between two normal populations while concurrently reducing computational complexity. Our methodology entails the systematic ranking of null hypotheses based on their Bayes factors, followed by the identification of all possible configurations of true and false ordered null hypotheses. By integrating the relevant non-nested models, we establish objective priors that enhance the posterior search for the appropriate family of true and false hypotheses, thereby effectively decreasing the search space from 2k to k + 1. We demonstrate the consistency of our proposed method and assess its performance through both simulated and empirical examples.