Large-scale dependent multiple testing via higher-order hidden Markov models.

Taking into account the local dependence structure in large-scale multiple testing is expected to improve both the efficiency of the testing procedure and the interpretability of scientific findings. The hidden Markov model (HMM), as an effective model to describe the sequential dependence, has been successfully applied to large-scale multiple testing with local correlations. However, in many applications, the first-order Markov chain is not flexible enough to capture the complexity of local correlations. To address this issue, this paper proposes a novel multiple testing procedure that uses a higher-order Markov chain to better characterize local correlations among tests. The proposed procedure is validated by theoretical results and simulation studies, which show that it outperforms its competitors in terms of power. Finally, a real data analysis is presented to demonstrate the favorable performance of the proposed procedure.