An optimal and flexible multiple hypotheses testing procedure is constructed for dependent data based on Bayesian techniques, aiming at handling two challenges, namely dependence structure and non-null distribution specification. Ignoring dependence among hypotheses tests may lead to loss of efficiency and bias in decision. Misspecification in the non-null distribution, on the other hand, can result in both false positive and false negative errors. Hidden Markov models are used to accommodate the dependence structure among the tests. Dirichlet mixture process prior is applied on the non-null distribution to overcome the potential pitfalls in distribution misspecification. The testing algorithm based on Bayesian techniques optimizes the false negative rate (FNR) while controlling the false discovery rate (FDR). The procedure is applied to pointwise and clusterwise analysis. Its performance is compared with existing approaches using both simulated and real data examples.

中文翻译：

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用于依赖大规模多重测试的贝叶斯隐马尔可夫模型

基于贝叶斯技术为相关数据构建了一个最优且灵活的多假设检验程序，旨在解决两个挑战，即依赖结构和非零分布规范。忽略假设检验之间的依赖性可能会导致决策效率下降和偏差。另一方面，非空分布中的错误指定会导致假阳性和假阴性错误。隐马尔可夫模型用于适应测试之间的依赖结构。Dirichlet 混合过程先验应用于非零分布，以克服分布错误指定中的潜在缺陷。基于贝叶斯技术的测试算法在控制错误发现率 (FDR) 的同时优化了假阴性率 (FNR)。该过程适用于逐点和聚类分析。使用模拟和真实数据示例将其性能与现有方法进行比较。