On the independence assumption underlying subjective bayesian updating

摘要

Current rule-based, expert systems must cope with uncertain, subjective information. This is normally done by some form of probabilistic reasoning. Duda, Hart, and Nilsson have proposed one such scheme that is based on Bayes' rule. In this note we provide further mathematical analysis related to this rule. In particular, we prove the following proposition: if the assumptions made in deriving Duda et al.'s scheme are satisfied, together with the additional assumptions that the space of hypotheses is mutually exclusive and exhaustive, then no updating can take place. However, since this latter assumption is rarely satisfied in realistic systems, we then indicate how our analysis changes as exclusivity and exhaustivity are relaxed.