# Bayesian inference in hierarchical models by combining independent posteriors

arXiv: https://arxiv.org/abs/1603.09272 · HTML: https://mlsanity.com/paper/1603.09272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2016.

## Built on by (most cited first, 1 of 1)

- [Approximate Gibbs Sampler for Efficient Inference of Hierarchical Bayesian Models for Grouped Count Data](https://mlsanity.com/paper/2211.15771/) (2022)

## Abstract (arXiv)

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.