On Default Priors for Robust Bayesian Estimation with Divergences.

Area of Science:

• Statistics
• Robust Bayesian Inference

Background:

• Outliers and contamination can significantly impact standard statistical estimation methods.
• Robust statistical methods aim to provide reliable inference in the presence of such data issues.
• Bayesian estimation traditionally relies on prior distributions, and their selection is crucial for objective inference.

Purpose of the Study:

• To develop objective prior distributions for robust Bayesian estimation.
• To investigate the properties of reference and moment matching priors under quasi-posterior distributions based on divergences.
• To ensure robustness against outliers and data contamination in Bayesian analysis.

Main Methods:

• Utilizing divergence measures, specifically the gamma-divergence, to define quasi-posterior distributions.
• Deriving and analyzing properties of reference and moment matching priors within this robust Bayesian framework.
• Conducting simulation studies to evaluate the performance of the proposed priors.

Main Results:

• The minimum gamma-divergence estimator demonstrates effectiveness against heavy data contamination.
• Proposed objective priors exhibit approximate robustness under specific contamination distribution conditions.
• Robustness is achieved without requiring prior knowledge of the contamination ratio.

Conclusions:

• Objective priors can be effectively developed for robust Bayesian estimation using divergence-based quasi-posterior distributions.
• The derived priors provide a robust framework for statistical modeling when data may contain outliers.
• This approach enhances the reliability of Bayesian inference in practical applications with imperfect data.