Parallel Markov Chain Monte Carlo for Bayesian Hierarchical Models with Big Data, in Two Stages

TL;DR

This paper introduces a two-stage parallel MCMC method tailored for Bayesian hierarchical models with big data, partitioning data by groups to improve efficiency and reduce computation time while maintaining accuracy.

Contribution

It extends existing parallel MCMC approaches by partitioning data by groups in hierarchical models, enhancing efficiency and scalability for big data applications.

Findings

Results closely match full data analysis.

Significant increase in MCMC efficiency.

Substantial reduction in computation time.

Abstract

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common for the full data set, with most parameters being group-specific. Thus, parallel Bayesian MCMC methods that take into account the structure of the model and split the full data set by groups rather than by observations are a more natural approach for analysis. Here, we adapt and extend a recently introduced two-stage Bayesian hierarchical modeling approach, and we partition complete data sets by groups. In stage 1, the group-specific parameters are estimated independently in parallel. The stage 1 posteriors are used as proposal distributions in stage 2, where the target distribution is the full model. Using three-level and four-level models, we show in both simulation and real data studies that results of our method agree closely with the full data analysis, with greatly increased MCMC efficiency and greatly reduced computation times. The advantages of our method versus existing parallel MCMC computing methods are also described.