Robust Bayesian Regression with Synthetic Posterior Distributions.

Area of Science:

• Statistics
• Bayesian inference
• Robust statistics

Background:

• Linear regression models are widely used but sensitive to outliers, complicating statistical inference.
• Existing frequentist robust methods can present challenges in statistical inference.

Purpose of the Study:

• To propose a Bayesian approach for robust inference in linear regression models.
• To develop a method that naturally assesses estimation uncertainty.
• To integrate robust variable selection and estimation.

Main Methods:

• Utilizing synthetic posterior distributions based on γ-divergence.
• Employing shrinkage priors for regression coefficients.
• Developing an efficient posterior computation algorithm using Bayesian bootstrap within Gibbs sampling.

Main Results:

• The proposed Bayesian method effectively handles outliers in linear regression.
• The approach allows for simultaneous robust variable selection and estimation.
• The method provides a natural way to assess estimation uncertainty via posterior distributions.

Conclusions:

• The proposed Bayesian approach offers a robust and flexible alternative for linear regression inference.
• This method enhances statistical modeling by addressing outlier sensitivity and enabling simultaneous variable selection.
• The developed algorithm is efficient for posterior computation.