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arXiv · 1904.04484

Meta-analysis of Bayesian analyses

Paul Blomstedt·Diego Mesquita·Omar Rivasplata·Jarno Lintusaari·Tuomas Sivula·Jukka Corander·Samuel Kaski
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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.

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Paul Blomstedt, Diego Mesquita, Omar Rivasplata, Jarno Lintusaari, Tuomas Sivula, Jukka Corander, Samuel Kaski. 2024-10-14. Meta-analysis of Bayesian analyses. https://doi.org/10.1214/24-ba1465

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