Bayesian Analysis of Finite Populations under Simple Random Sampling

Area of Science:

• Statistics
• Survey Methodology
• Bayesian Inference

Background:

• Established statistical methods for finite population sampling exist for decades.
• The Bayesian approach is widely adopted, yet a default procedure for Bayesian survey sampling is lacking, especially for mixed variable types.
• Existing methods may not adequately handle both continuous and discrete variables within a Bayesian framework.

Purpose of the Study:

• To discuss the Bayesian analysis of samples from finite populations.
• To review the relationship between Bayesian analysis and the superpopulation concept.
• To propose a new nonparametric approach for Bayesian survey sampling applicable to diverse data types.

Main Methods:

• The study reviews existing Bayesian analysis principles for finite populations.
• It explores the connection between Bayesian inference and superpopulation models.
• A novel nonparametric Bayesian approach is developed and presented.

Main Results:

• The proposed nonparametric method provides a default procedure for Bayesian survey sampling.
• It effectively handles both continuous and discrete variables.
• The approach allows for inferences on population quantiles, means, and totals.

Conclusions:

• The developed Bayesian survey sampling method offers a flexible and unified approach.
• It provides rapid inferences, beneficial for time-sensitive analyses like electoral quick counts.
• This nonparametric Bayesian framework enhances statistical capabilities for finite population studies.