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

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Large-scale multiple testing requires accounting for local dependence structures for improved efficiency and interpretability.
• Hidden Markov models (HMMs) have been used for sequential dependence in multiple testing but often lack flexibility.
• First-order Markov chains may not fully capture complex local correlations in real-world data.

Purpose of the Study:

• To propose a novel multiple testing procedure utilizing higher-order Markov chains.
• To enhance the characterization of local correlations among tests in large-scale settings.
• To improve the power and interpretability of multiple testing procedures.

Main Methods:

• Development of a multiple testing procedure based on higher-order Markov chains.
• Theoretical validation of the proposed method.
• Simulation studies to compare performance against existing methods.

Main Results:

• The proposed higher-order Markov chain-based procedure demonstrates superior power compared to existing methods.
• Theoretical results support the efficacy of the novel approach.
• Simulation studies confirm the enhanced performance.

Conclusions:

• Higher-order Markov chains offer a more flexible and powerful approach to modeling local correlations in large-scale multiple testing.
• The proposed procedure provides a valuable tool for improving statistical analysis in various scientific fields.
• Real-world data analysis confirms the practical utility and favorable performance of the new method.