Bayesian inference in hierarchical models by combining independent posteriors

TL;DR

This paper introduces a computationally efficient method for Bayesian inference in hierarchical models by combining independently obtained posteriors, enabling parallel processing and faster convergence for complex or large-scale data sources.

Contribution

It proposes a novel approach that uses independent source-specific posteriors as observed data in a scaled likelihood hierarchical model, improving computational efficiency.

Findings

Method speeds up convergence compared to full hierarchical inference

Enables parallel processing of source-specific inferences

Effective on both simulated and real datasets

Abstract

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex, or if the number of sources is very large. To facilitate computation, we propose an approach, where inference is first made independently for the parameters of each data set, whereupon the obtained posterior samples are used as observed data in a substitute hierarchical model, based on a scaled likelihood function. Compared to direct inference in a full hierarchical model, the approach has the advantage of being able to speed up convergence by breaking down the initial large inference problem into smaller individual subproblems with better convergence properties. Moreover it enables parallel processing of the possibly complex inferences of the source-specific parameters, which may otherwise create a computational bottleneck if processed jointly as part of a hierarchical model. The approach is illustrated with both simulated and real data.