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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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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

This summary is machine-generated.

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.

Keywords:

Bagging Bernstein–Von Mises theorem Jeffrey conditionalization Primary 62F15, 62F40 bootstrap model misspecification overlap probability secondary 62A01, 62F35 uncertainty calibration

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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.