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Updated: Jan 12, 2026
04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
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Reproducible parameter inference using bagged posteriors
Jonathan H Huggins1, Jeffrey W Miller2
1Department of Mathematics & Statistics, Boston University.
Electronic Journal of Statistics
|November 7, 2025
Summary
Bayesian posteriors struggle with uncertainty quantification and reproducibility under model misspecification. A new method, BayesBag, averages posteriors from bootstrapped data, improving reproducibility and uncertainty quantification for Bayesian analysis.
Area of Science:
- Statistics
- Computational Statistics
Background:
- Model misspecification in Bayesian statistics can lead to improper uncertainty quantification and a lack of reproducibility.
- Standard Bayesian posteriors may yield contradictory results on independent datasets when the model is misspecified.
Purpose of the Study:
- To define a criterion for reproducible uncertainty quantification under model misspecification.
- To introduce a practical method for improving the reproducibility of Bayesian posteriors.
Main Methods:
- Defined a lower bound on the overlap probability of credible sets from independent datasets.
- Proposed "BayesBag," an averaging of Bayesian posterior distributions conditioned on bootstrapped datasets.
- Proved a Bernstein-Von Mises theorem for the bagged posterior.
Main Results:
- Standard Bayesian posteriors can violate the established overlap bound under misspecification.
- BayesBag typically satisfies the overlap lower bound, enhancing reproducibility.
- The bagged posterior exhibits asymptotic normality.
Conclusions:
- BayesBag offers an easy-to-use and widely applicable solution for reproducible uncertainty quantification in Bayesian modeling, even under misspecification.
- The method was validated through simulations and a real-world application in crime rate prediction.
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