Two-group Poisson-Dirichlet mixtures for multiple testing.

Area of Science:

• Statistical Inference
• Bayesian Nonparametrics
• High-Dimensional Data Analysis

Background:

• Simultaneous hypothesis testing is crucial for high-dimensional data.
• Efron's two-group model uses mixture distributions for significance testing.
• Existing Bayesian nonparametric methods often use Dirichlet Process mixtures.

Purpose of the Study:

• To investigate the use of two-parameter Poisson-Dirichlet Process mixtures for large-scale hypothesis testing.
• To develop a more flexible and effective Bayesian nonparametric approach.
• To improve the separation of null and alternative distributions in hypothesis testing.

Main Methods:

• Employed mixtures of two-parameter Poisson-Dirichlet Processes.
• Utilized nonlocal prior densities to enhance component separation.
• Derived a closed-form expression for the exchangeable partition probability function.
• Implemented a straightforward Markov Chain Monte Carlo (MCMC) method.

Main Results:

• Demonstrated increased flexibility and effectiveness of the proposed method.
• Achieved better separation between mixture components using nonlocal priors.
• The derived closed-form expression facilitated MCMC implementation.
• The method showed strong performance in simulation studies.

Conclusions:

• The proposed two-parameter Poisson-Dirichlet Process mixture model offers a powerful tool for large-scale hypothesis testing.
• This approach provides a flexible and effective alternative to existing methods for analyzing high-dimensional data.
• The model was successfully applied to real-world datasets in cancer research and microbiome studies.