An Approach to Incorporate Subsampling into a Generic Bayesian Hierarchical Model

Area of Science:

• Statistics
• Computational Statistics
• Bayesian Inference

Background:

• The proliferation of big data presents significant computational challenges for traditional statistical methods.
• Bayesian statisticians require flexible approaches to handle large datasets without compromising model integrity.

Purpose of the Study:

• To introduce a novel method for incorporating subsampling directly into Bayesian hierarchical models.
• To enable Bayesian analysis of large datasets by addressing computational limitations.

Main Methods:

• Introduction of a "data subset model" within the existing "data model, process model, and parameter model" framework.
• Constructive specification of hyperparameters to meet computational constraints, effectively calibrating models to hardware.
• Evaluation of statistical properties including propriety, partial sufficiency, and semi-parametric characteristics.

Main Results:

• Demonstration of the data subset model's ability to integrate subsampling without additional restrictive assumptions.
• Assessment of subsampling consequences using simulated datasets and analysis across different computing environments.
• Application to a 10-gigabyte US Census Bureau Public Use Micro-Sample (PUMS) dataset.

Conclusions:

• The proposed data subset model offers a practical solution for Bayesian analysis of big data.
• The method allows for pre-specified computational time constraints, balancing statistical accuracy and efficiency.
• This approach facilitates the application of Bayesian hierarchical models to previously intractable large-scale datasets.