Bayesian inference provides principled uncertainty quantification but is often limited by 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. Additionally 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 model's implicit latent model. The MGP provides the 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：贝叶斯推断提供了原则性的不确定性量化方法，但常受限于先验分布与似然函数设定的挑战。鞅后验（MGP）（Fong等人，2023）通过用预测规则替代这些要求，提供了一种替代方案。此外，MGP将推断聚焦于通过损失函数定义的参数上。这一框架在基础Transformer时代尤为契合：实践者越来越多地利用如TabPFN等具备先进能力的模型，但通常需要为科学估计量$θ$提供认知不确定性，而该估计量不必参数化模型的隐式潜模型。MGP提供了恢复这些后验分布的机制。我们提出了TabMGP——一种基于TabPFN的、面向表格数据的MGP方法。TabMGP能产生接近名义覆盖度的可信区间，其性能通常优于人工构建的MGP方案及标准贝叶斯基线方法。