🤖 AI Summary
This study addresses the challenges of inaccurate uncertainty quantification and insufficient coverage of confidence sets in predictive resampling by proposing a bagged martingale posterior method. This approach integrates Bayesian inference, bootstrap techniques, and high-dimensional quantile modeling to achieve conservative calibration by initiating predictive paths from random bootstrap samples and aggregating the results. Its core innovation lies in substantially improving calibration accuracy without additional simulation costs, thereby overcoming the reliance of conventional methods on algorithmic tuning. Experimental results demonstrate that the proposed method delivers computationally efficient and conservatively calibrated uncertainty quantification in complex scenarios, such as sparse high-dimensional regression.
📝 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.