# Meta-analysis of Bayesian analyses

arXiv: https://arxiv.org/abs/1904.04484 · HTML: https://mlsanity.com/paper/1904.04484/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2019.

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

- [Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference](https://mlsanity.com/paper/2312.05153/) (2023)

## Abstract (arXiv)

Meta-analysis aims to generalize results from multiple related statistical analyses through a combined analysis. While the natural outcome of a Bayesian study is a posterior distribution, traditional Bayesian meta-analyses proceed by combining summary statistics (i.e., point-valued estimates) computed from data. In this paper, we develop a framework for combining posterior distributions from multiple related Bayesian studies into a meta-analysis. Importantly, the method is capable of reusing pre-computed posteriors from computationally costly analyses, without needing the implementation details from each study. Besides providing a consensus across studies, the method enables updating the local posteriors post-hoc and therefore refining them by sharing statistical strength between the studies, without rerunning the original analyses. We illustrate the wide applicability of the framework by combining results from likelihood-free Bayesian analyses, which would be difficult to carry out using standard methodology.