Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when there exist model misspecifications in prior distributions and/or data distributions, the direct application of Bayes' rule is questionable. Philosophically, the key is to balance the relative importance of prior and data distributions when calculating posterior distributions: if prior (resp. data) distributions are overly conservative, we should upweight the prior belief (resp. data evidence); if prior (resp. data) distributions are overly opportunistic, we should downweight the prior belief (resp. data evidence). This paper derives a generalized Bayes' rule, called uncertainty-aware Bayes' rule, to technically realize the above philosophy, i.e., to combat the model uncertainties in prior distributions and/or data distributions. Simulated and real-world experiments showcase the superiority of the presented uncertainty-aware Bayes' rule over the conventional Bayes' rule: In particular, the uncertainty-aware Kalman filter, the uncertainty-aware particle filter, and the uncertainty-aware interactive multiple model filter are suggested and validated.

翻译：贝叶斯规则已催生了统计信号处理与统计机器学习领域众多强大的算法。然而，当先验分布和/或数据分布存在模型误设时，直接应用贝叶斯规则便值得商榷。从哲学层面而言，关键在于计算后验分布时平衡先验分布与数据分布的相对重要性：若先验分布（或数据分布）过于保守，则应提升先验信念（或数据证据）的权重；若先验分布（或数据分布）过于机会主义，则应降低先验信念（或数据证据）的权重。本文推导出一种称为"不确定性感知贝叶斯规则"的广义贝叶斯规则，从技术层面实现上述哲学思想，即对抗先验分布和/或数据分布中的模型不确定性。模拟实验与真实世界实验均展示了所提出的不确定性感知贝叶斯规则相较于传统贝叶斯规则的优越性：具体而言，本文验证了不确定性感知卡尔曼滤波器、不确定性感知粒子滤波器及不确定性感知交互式多模型滤波器的有效性。