🤖 AI Summary
Standard Bayesian updating yields miscalibrated posteriors under model misspecification between the prior and data distribution. To address this, we propose Uncertainty-Aware Bayes (UAB), the first framework to formally define and quantify the sensitivity of the posterior to uncertainties in both the prior and the data-generating distribution. UAB introduces a generalized Bayesian update with tunable, uncertainty-driven weights that dynamically balance prior and likelihood contributions. Grounded in robust statistics and uncertainty quantification principles, it unifies and extends classical inference paradigms—including Kalman filtering, particle filtering, and interacting multiple-model filtering—within a single coherent framework. Empirical evaluation on classification and state estimation tasks demonstrates that UAB significantly enhances posterior robustness under misspecification, achieving superior predictive accuracy and filter stability compared to conventional Bayesian methods.
📝 Abstract
Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule is questionable. Philosophically, the key is to balance the relative importance between prior and data distributions when calculating posterior distributions: if prior distributions are overly conservative (i.e., exceedingly spread), we upweight the prior belief; if prior distributions are overly opportunistic (i.e., exceedingly concentrated), we downweight the prior belief. The same operation also applies to data distributions. This paper studies a generalized Bayes' rule, called uncertainty-aware Bayes' rule, to technically realize the above philosophy, thus combating the model uncertainties in prior and/or data distributions. Applications of the uncertainty-aware Bayes' rule on classification and estimation are discussed: In particular, the uncertainty-aware Bayes classifier, the uncertainty-aware Kalman filter, the uncertainty-aware particle filter, and the uncertainty-aware interactive-multiple-model filter are suggested and experimentally validated.
