For robustness toward model misspecification, the generalized posterior inference approach modifies the likelihood term by raising it to the power of a learning rate, thereby adjusting the spread of the posterior. This paper proposes a computationally efficient strategy for selecting an appropriate learning rate. The proposed approach builds upon the generalized posterior calibration (GPC) algorithm introduced by Syring and Martin (2019) [Biometrika, Volume 106, Issue 2, pp. 479-486], which is designed to select the learning rate to achieve the nominal frequentist coverage. This algorithm, which evaluates the coverage probability based on bootstrap samples, suffers from high computational costs due to the need for repeated posterior simulations for bootstrap samples. To address this limitation, the study proposes an algorithm that combines elements of the GPC algorithm with the sequential Monte Carlo (SMC) sampler. By leveraging the similarity between the learning rate in generalized posterior inference and the inverse temperature in SMC sampling, the proposed algorithm efficiently calibrates the posterior distribution with less computational cost. For demonstration, the proposed algorithm was applied to several statistical learning models.

翻译：针对模型误设定的鲁棒性问题，广义后验推断方法通过对似然项进行学习率幂次调整，从而改变后验分布的分散程度。本文提出了一种高效计算策略来选择合适的学习率。该方法基于Syring和Martin（2019）[Biometrika, 第106卷, 第2期, 第479-486页]提出的广义后验校准（GPC）算法，该算法旨在选择学习率以实现名义频率覆盖。原始算法基于自助法样本评估覆盖概率，由于需要对每个自助法样本重复进行后验模拟，导致计算成本高昂。为克服这一局限，本研究提出了一种融合GPC算法与序贯蒙特卡洛（SMC）采样器要素的算法。通过利用广义后验推断中学习率与SMC采样中逆温度参数之间的相似性，所提出的算法能够以较低计算成本高效校准后验分布。为验证效果，该算法被应用于多个统计学习模型。