A Markov chain representation of the multiple testing problem.

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Multiple hypothesis testing is a significant challenge in analyzing large datasets.
• Existing methods can be computationally intensive and complex.
• Bayes Factors offer a probabilistic approach but often require precise prior specification.

Purpose of the Study:

• To develop a computationally efficient and interpretable method for multiple hypothesis testing.
• To leverage Markov processes for approximating posterior probabilities of hypotheses.
• To enable robust analysis of large-scale genomic data.

Main Methods:

• Representing multiple hypothesis testing as a Markov process.
• Utilizing Bayes Factors, even when defined up to an unknown constant.
• Forming a Markov transition kernel using default priors or calibrated p-values.
• Applying the method to gene expression data (microarray, RNA-seq).

Main Results:

• The Markov process effectively identifies the most probable set of non-null hypotheses.
• The approach yields interpretable results with simple formulas.
• Posterior probabilities for all alternative hypotheses can be obtained.
• The method is suitable for large datasets common in genomics.

Conclusions:

• This Markov process approach offers a powerful and accessible tool for multiple hypothesis testing.
• It simplifies the analysis of complex biological data, particularly in genomics.
• The method provides a robust alternative for hypothesis evaluation in high-dimensional studies.