CENTER-ADJUSTED INFERENCE FOR A NONPARAMETRIC BAYESIAN RANDOM EFFECT DISTRIBUTION.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Dirichlet process (DP) priors are widely used in semiparametric Bayesian random effect models.
• DP priors present identifiability challenges for fixed effects and variance components due to a non-zero mean assumption.
• This complicates interpretation and inference in mixed-effects models.

Purpose of the Study:

• To propose an adjusted inference method for semiparametric Bayesian models using Dirichlet process priors.
• To address the identifiability problems associated with DP priors in mixed-effects models.
• To provide a computationally efficient adjustment technique.

Main Methods:

• Developed a post-processing technique based on analytic evaluation of DP moments.
• Integrated the moment adjustment into Markov chain Monte Carlo (MCMC) simulations.
• Validated the method through simulation studies in linear and logistic mixed-effects models.
• Applied the method to a prostate-specific antigen dataset.

Main Results:

• The proposed adjustment method effectively resolves identifiability issues in DP-mixed models.
• The adjustment can be seamlessly incorporated into MCMC simulations with minimal computational overhead.
• Simulation studies demonstrated the procedure's good performance in both linear and logistic models.
• An R function is provided for practical implementation.

Conclusions:

• The post-processing adjustment offers a practical solution for inference challenges with DP priors in Bayesian models.
• This method enhances the interpretability and reliability of fixed effects and variance components.
• The approach is computationally efficient and readily applicable in statistical software.