Dir-GLM: A Bayesian GLM With Data-Driven Reference Distribution.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Classical generalized linear models (GLM) lack flexibility.
• Semi-parametric generalized linear models (SPGLM) enhance flexibility by incorporating a baseline distribution.
• Existing maximum-likelihood inference methods (GLDRM) struggle with generating certain inference summaries, like uncertainty in exceedance probabilities.

Purpose of the Study:

• To propose a Bayesian model-based approach for SPGLM inference.
• To address limitations in generating inference summaries, particularly for model-derived functionals.
• To improve estimation of critical parameters such as exceedance probabilities for clinical decision-making.

Main Methods:

• Developed a Bayesian framework by placing a Dirichlet prior on the baseline distribution.
• Established consistency and asymptotic normality results for the canonical parameter.
• Utilized simulation studies and real-world data from an aging research study for validation.

Main Results:

• The proposed Bayesian method demonstrates comparable or superior performance to GLDRM.
• The framework effectively handles uncertainty in estimation for model-derived functionals.
• Consistency and asymptotic normality were established for the canonical parameter.

Conclusions:

• The Bayesian approach offers a robust alternative for SPGLM inference.
• This method is particularly advantageous for small sample training data or sparse-data scenarios.
• The proposed framework enhances the utility of SPGLMs in statistical modeling and decision-making contexts.