Bagged Martingale Posteriors: Calibrated Uncertainty Quantification for Predictive Resampling
Abstract
Martingale posteriors and related predictive resampling methods replace the likelihood--prior pair used within Bayesian inference with a predictive model for future observations. These methods are simple to implement and increasingly popular due to their computational efficiency, but little is known about their ability to accurately quantify uncertainty. In this work, we study the concentration and calibration properties of the martingale posterior for general functionals, and show that credible sets can systematically undercover if the predictive algorithms are not carefully tuned. We propose a simple remedy: the bagged martingale posterior. Rather than starting every predictive path from the observed sample, we start the paths from random bootstrap resamples of the data and then amalgamate the resulting draws. Critically, this approach incurs no additional {simulation} cost compared to standard predictive resampling, and delivers conservatively calibrated credible sets. This scalability enables application to a range of challenging examples, including sparse high-dimensional regression and nonparametric conditional quantile models.
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BibTeX
@misc{wang2026bagged,
title = {{Bagged Martingale Posteriors: Calibrated Uncertainty Quantification for Predictive Resampling}},
author = {Hui Wang and Edwin Fong and David T. Frazier},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30622},
eprint = {2609.30622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30622},
}
RIS
TY - UNPB
TI - Bagged Martingale Posteriors: Calibrated Uncertainty Quantification for Predictive Resampling
AU - Hui Wang
AU - Edwin Fong
AU - David T. Frazier
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30622
UR - https://arxiv.org/abs/2609.30622
AB - Martingale posteriors and related predictive resampling methods replace the likelihood--prior pair used within Bayesian inference with a predictive model for future observations. These methods are simple to implement and increasingly popular due to their computational efficiency, but little is known about their ability to accurately quantify uncertainty. In this work, we study the concentration and calibration properties of the martingale posterior for general functionals, and show that credible sets can systematically undercover if the predictive algorithms are not carefully tuned. We propose a simple remedy: the bagged martingale posterior. Rather than starting every predictive path from the observed sample, we start the paths from random bootstrap resamples of the data and then amalgamate the resulting draws. Critically, this approach incurs no additional {simulation} cost compared to standard predictive resampling, and delivers conservatively calibrated credible sets. This scalability enables application to a range of challenging examples, including sparse high-dimensional regression and nonparametric conditional quantile models.
ER -