In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The first is generalized Bayesian inference, which introduces a learning rate parameter to enhance robustness against model misspecifications. The second is Gibbs posterior inference, which formulates inferential problems using generic loss functions rather than probabilistic models. In such approaches, it is necessary to calibrate the spread of the posterior distribution by selecting a learning rate parameter. The study aims to enhance the generalized posterior calibration (GPC) algorithm proposed by [1]. Their algorithm chooses the learning rate to achieve the nominal frequentist coverage probability, but it is computationally intensive because it requires repeated posterior simulations for bootstrap samples. We propose a more efficient version of the GPC inspired by sequential Monte Carlo (SMC) samplers. A target distribution with a different learning rate is evaluated without posterior simulation as in the reweighting step in SMC sampling. Thus, the proposed algorithm can reach the desirable value within a few iterations. This improvement substantially reduces the computational cost of the GPC. Its efficacy is demonstrated through synthetic and real data applications.

翻译：在统计学习领域，日益增长的数据获取量与不断提升的模型复杂度对方法的稳健性提出了更高要求。本文针对这一趋势，探讨了稳健贝叶斯方法的两个分支：其一是广义贝叶斯推断，通过引入学习率参数以增强对模型设定错误的稳健性；其二是吉布斯后验推断，该方法采用通用损失函数而非概率模型来构建推断问题。在此类方法中，需要通过选择学习率参数来校准后验分布的离散程度。本研究旨在改进文献[1]提出的广义后验校准算法。原算法通过选择学习率以实现名义频率主义覆盖概率，但由于需要对自助法样本进行重复后验模拟，计算负担较重。受序贯蒙特卡罗采样器启发，我们提出了一种更高效的广义后验校准算法。该算法借鉴SMC采样中的重加权步骤，无需后验模拟即可评估具有不同学习率的目标分布。因此，所提算法能在少量迭代内达到目标值，显著降低了广义后验校准的计算成本。通过合成数据与真实数据的应用验证了该方法的有效性。