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 <i>k</i> + 1. We demonstrate the consistency of our proposed method and assess its performance through both simulated and empirical examples.

贝叶斯多重检验（Bayesian multiple testing）问题需要对所有可能的真零假设与假零假设的配置情况进行考察，随着假设数量的增加，该任务的复杂度会显著提升。为解决这一问题，我们提出了一种客观贝叶斯多重检验流程，旨在实现两个正态总体间的均值比较，同时降低计算复杂度。我们的方法首先基于贝叶斯因子（Bayes factor）对零假设进行系统性排序，随后识别所有经排序后的零假设为真或为假的可能配置。通过整合相关的非嵌套模型，我们构建了客观先验分布，以优化针对合适的真假假设族的后验搜索，从而将搜索空间从2^k有效缩减至k+1。我们验证了所提方法的一致性，并通过模拟案例与实证案例评估了其性能表现。