2023/07/13 by Michele Caprio, Yusuf Sale, Caprio, Michele +5 · 1 citation
Computer Science · Engineering · #68T37 #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.2307.06831
openalex publication_date 2023/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In their seminal 1990 paper, Wasserman and Kadane establish an upper bound for the Bayes' posterior probability of a measurable set A, when the prior lies in a class of probability measures P and the likelihood is precise. They also give a sufficient condition for such upper bound to hold with equality. In this paper, we introduce a generalization of their result by additionally addressing uncertainty related to the likelihood. We give an upper bound for the posterior probability when both the prior and the likelihood belong to a set of probabilities. Furthermore, we give a sufficient condition for this upper bound to become an equality. This result is interesting on its own, and has the potential of being applied to various fields of engineering (e.g. model predictive control), machine learning, and artificial intelligence.