A nonparametric empirical Bayes framework for large-scale multiple testing.

Area of Science:

• Statistics
• Bayesian Inference
• Computational Statistics

Background:

• Hierarchical models are widely used but can be inflexible.
• Existing methods may struggle with accurate density estimation in mixture models, particularly in the tails.
• Empirical Bayes approaches offer advantages in hypothesis testing with large datasets.

Purpose of the Study:

• To develop a flexible and identifiable 2-groups model using hierarchical Bayes.
• To introduce a computationally efficient method for estimating model parameters, including nonparametric distributions.
• To establish a novel empirical Bayes testing procedure (PRtest) for improved data analysis.

Main Methods:

• Utilized a hierarchical Bayes framework for a flexible 2-groups model.
• Employed a predictive recursion (PR) marginal likelihood procedure for efficient parameter estimation.
• Developed a nonparametric empirical Bayes testing procedure (PRtest) based on local false discovery rates.

Main Results:

• PRtest demonstrated a better fit in the tails of mixture distributions compared to existing methods.
• The method efficiently estimates model parameters, including nonparametric mixing distributions.
• Simulations and real data analyses confirmed the advantages of PRtest.

Conclusions:

• PRtest provides a more realistic and accurate approach to hypothesis testing.
• The method's ability to handle complex mixture distributions enhances its applicability in various scientific fields.
• PRtest offers a computationally efficient and statistically robust alternative for empirical Bayes inference.