Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and propose a new analog, as the Bayes rule under a form of balanced loss function, that combines elements of standard parametric inference with fidelity of the data to the model. Our development is general, for essentially any regression setting with independent outcomes. Being the large-sample equivalent of its frequentist counterpart, we show by simulation that Bayesian robust standard error estimates can faithfully quantify the variability of parameter estimates even under model misspecification -- thus retaining the major attraction of the original frequentist version. We demonstrate our Bayesian analog of standard error estimates when studying the association between age and systolic blood pressure in NHANES.

翻译：对于许多频率学派方法，存在大样本贝叶斯类比方法，但广泛使用的"三明治"或"稳健"方差估计的贝叶斯类比方法却鲜为人知。本文回顾了现有的三明治方差估计的贝叶斯类比方法，并提出了一种新的类比方法——作为平衡损失函数形式下的贝叶斯规则，该方法结合了标准参数推断与数据对模型拟合优度的要素。我们的发展具有普适性，基本适用于任何具有独立结果变量的回归场景。作为频率学派对应方法的大样本等价形式，我们通过模拟表明，即使在模型设定错误的情况下，贝叶斯稳健标准误估计也能准确量化参数估计的变异性——从而保留了原始频率学派版本的主要吸引力。我们在研究NHANES数据中年龄与收缩压的关联时，展示了贝叶斯类比标准误估计的应用。