Uncertainty-Aware Bayes' Rule and Its Applications

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.