BIVARIATE HIERARCHICAL BAYESIAN MODEL FOR COMBINING SUMMARY MEASURES AND THEIR UNCERTAINTIES FROM MULTIPLE SOURCES.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Combining estimates from multiple data sources is crucial.
• Existing methods may not fully account for the uncertainty in variance estimation.
• The correlation between estimates and their variances is often overlooked.

Purpose of the Study:

• To propose a bivariate hierarchical Bayesian model for combining estimates.
• To jointly model estimates and their estimated variances, including their correlation.
• To evaluate the model's performance against existing methods.

Main Methods:

• Developed a bivariate hierarchical Bayesian model.
• Jointly modeled estimates and their estimated variances.
• Conducted simulations to assess model performance under various correlation scenarios.

Main Results:

• The proposed bivariate Bayesian model demonstrated effective performance.
• The model accurately incorporates the uncertainty in variance estimation.
• Comparison with other methods showed advantages in different correlation scenarios.

Conclusions:

• The bivariate hierarchical Bayesian model offers a robust approach for combining estimates.
• The model's ability to handle correlations between estimates and variances is a key strength.
• The model is applicable to diverse fields like PET imaging, meta-analysis, and small area estimation.