Meta-analysis of Bayesian analyses

TL;DR

This paper introduces a novel Bayesian meta-analysis framework that combines posterior distributions from multiple studies, allowing for efficient integration, updating, and sharing of statistical strength without re-analyzing original data.

Contribution

It presents a new method for combining and updating Bayesian posteriors across studies, including likelihood-free analyses, without needing detailed data or re-computation.

Findings

Enables combining pre-computed posteriors from different studies.

Allows post-hoc updating and refinement of local posteriors.

Facilitates meta-analysis of likelihood-free Bayesian methods.

Abstract

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.