On some problems of Bayesian region construction with guaranteed coverages

Area of Science:

• Statistics
• Bayesian Inference
• Statistical Modeling

Background:

• Constructing reliable statistical regions with guaranteed coverage probability is a persistent challenge.
• Existing confidence regions can suffer from undesirable properties, such as improper regions.

Purpose of the Study:

• To develop a Bayesian methodology for creating regions with guaranteed coverage probability for parameters of interest.
• To offer a method that controls both prior coverage probability and the accuracy of Bayesian confidence intervals.
• To address limitations of existing methods, particularly the issue of improper regions.

Main Methods:

• Utilizing Bayesian principles to define regions of interest.
• Integrating out nuisance parameters using conditional priors.
• Controlling coverage probability and accuracy by adjusting sample size.

Main Results:

• The developed regions are Bayesian in nature, offering Bayesian confidences.
• Prior coverage probability and accuracy can be precisely controlled via sample size.
• The approach guarantees the avoidance of improper regions, a common issue in other methods.

Conclusions:

• The proposed Bayesian framework provides a robust method for constructing reliable statistical regions.
• This approach enhances the trustworthiness of statistical inferences by controlling key performance metrics.
• It offers a significant improvement over methods prone to generating improper regions.