Finite Population Survey Sampling: An Unapologetic Bayesian Perspective

Area of Science:

• Statistics
• Statistical Inference
• Computational Statistics

Background:

• Finite population sampling often assumes independent units, which is unrealistic in many complex scenarios.
• Bayesian hierarchical models offer a flexible framework for incorporating prior information and complex data structures.
• Existing methods may not adequately address dependencies between population units.

Purpose of the Study:

• To provide perspectives on Bayesian inference for finite population quantities with complex dependencies.
• To extend inferential frameworks to accommodate dependent units and nonignorable responses.
• To illustrate applications using graphical models and spatial processes.

Main Methods:

• Overview of Bayesian hierarchical models, including those yielding Horvitz-Thompson estimators.
• Introduction of frameworks for ignorable and nonignorable response mechanisms in dependent finite populations.
• Application of multivariate dependencies using graphical models and spatial processes.

Main Results:

• Demonstration of inferential frameworks for complex dependencies in finite populations.
• Presentation of methodologies for handling both ignorable and nonignorable responses.
• Illustrative analyses of spatial finite populations showcasing the discussed methods.

Conclusions:

• Bayesian inference provides a robust approach for finite populations with complex dependencies.
• The proposed frameworks enhance the ability to model and analyze dependent data structures.
• Graphical models and spatial processes are valuable tools for understanding multivariate dependencies.