Bayesian inference provides principled uncertainty quantification but is often limited by the challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these requirements with a predictive rule. In addition, the MGP focuses inference on parameters defined through a loss function. This framework is especially resonant in the era of foundation transformers; practitioners increasingly leverage models like TabPFN for their state-of-the-art capabilities, yet often require epistemic uncertainty for a scientific estimand $θ$ that need not parameterise the implicit latent model. The MGP provides a mechanism to recover these posterior distributions. We introduce TabMGP, an MGP built on TabPFN for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both handcrafted MGP constructions and standard Bayesian baselines.

翻译：贝叶斯推断为不确定性量化提供了严谨的理论基础，但常受制于先验分布和似然函数设定的挑战。马氏过程后验（Fong等, 2023）通过以预测规则替代上述需求而提出替代方案。此外，MGP将推断聚焦于通过损失函数定义的参数。该框架在基础Transformer时代尤为契合——实践者日益借助TabPFN等模型的前沿能力，却常需针对科学推断目标θ的认知不确定性，而该参数无需参数化隐含的潜在模型。MGP提供了恢复这些后验分布的机制。我们提出TabMGP——一种基于TabPFN构建的表格数据MGP。TabMGP生成的置信集具有接近名义覆盖率的置信度，且其性能通常优于手工设计的MGP构造及标准贝叶斯基线方法。