Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior elicitation, likelihood misspecification, and computational burden. The martingale posterior (MGP, Fong et al., 2023) offers an alternative, replacing prior-likelihood elicitation with a predictive rule - namely, a sequence of one-step-ahead predictive distributions - for forward data generation. The utility of MGPs depends on the choice of predictive rule, yet the literature has offered few compelling examples. Foundation transformers are well-suited here, as their autoregressive generation mirrors this forward simulation and their general-purpose design enables rich predictive modeling. We introduce TabMGP, an MGP built on TabPFN, a transformer foundation model that is currently state-of-the-art for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both existing MGP constructions and standard Bayes.

翻译：贝叶斯推断提供了原则性的不确定性量化方法，但常受限于先验设定、似然函数误设及计算负担等挑战。鞅后验（MGP，Fong等人，2023）提供了一种替代方案，它用预测规则——即一系列一步向前预测分布——替代先验-似然设定，以进行前向数据生成。MGP的效用取决于预测规则的选择，但现有文献中鲜有令人信服的实例。基础Transformer模型在此场景中具有天然优势，其自回归生成机制与前向模拟过程相契合，且通用型设计支持丰富的预测建模。本文提出TabMGP，这是一种基于TabPFN构建的MGP方法——TabPFN是目前在表格数据领域达到最先进水平的Transformer基础模型。TabMGP生成的置信集具有接近名义水平的覆盖度，且通常优于现有MGP构建方法与标准贝叶斯方法。