发表机构
Monash University; University of Hong Kong（莫纳什大学; 香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出袋装鞅后验方法，通过从数据自助重采样启动预测路径并合并结果，在不增加模拟成本的情况下改善鞅后验的可信集校准，适用于稀疏高维回归等挑战性场景。
AI 中文摘要
鞅后验及相关的预测重采样方法将贝叶斯推断中的似然-先验对替换为对未来观测的预测模型。这些方法实现简单，且因其计算效率高而日益流行，但对其准确量化不确定性的能力知之甚少。在本工作中，我们研究了一般泛函的鞅后验的集中性和校准性质，并表明如果预测算法未仔细调整，可信集可能系统性覆盖不足。我们提出一个简单的补救措施：袋装鞅后验。我们不是从观测样本开始每条预测路径，而是从数据的随机自助重采样开始这些路径，然后合并得到的抽取结果。关键的是，与标准预测重采样相比，这种方法不产生额外的模拟成本，并提供保守校准的可信集。这种可扩展性使其能够应用于一系列具有挑战性的例子，包括稀疏高维回归和非参数条件分位数模型。
英文摘要
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.
