Generalized Empirical Bayes Modeling via Frequentist Goodness of Fit

Area of Science:

• Statistics
• Data Science

Background:

• Modern Bayesian statistics faces challenges in prior selection and integrating with frequentist methods.
• Existing approaches may lack a unified framework for data analysis.

Purpose of the Study:

• To propose a novel framework,
• Bayes via goodness-of-fit,
• to address fundamental questions in Bayesian statistics.
• To develop a consolidated Bayes-frequentist data analysis workflow.

Main Methods:

• The proposed
• Bayes via goodness-of-fit
• framework is presented as a general approach.
• The framework is applied to various probability models.

Main Results:

• The
• Bayes via goodness-of-fit
• framework offers a principled method for prior distillation.
• It facilitates a consolidated Bayes-frequentist data analysis workflow.
• Demonstrated utility across clinical trials, metrology, insurance, medicine, and ecology.

Conclusions:

• The
• Bayes via goodness-of-fit
• framework provides a unique perspective and practical tool for data science.
• It enhances the effectiveness of data analysis by integrating Bayesian and frequentist principles.