Revisiting Bayes’ Rule and Evidence: Notional Events vs. Real Data

The paper undertakes a conceptual scrutiny of Bayes’ rule in terms of the nature and interpretation of its probabilistic components, which reveals that there is nothing obvious or self-evident about it. First, it is not an instantiation of the conditional probability formula because (i) it involves conditioning on the unobservable event (a hypothesis), and (ii) it ignores the gap between Plato’s world () and the real world of evidence  by assuming that the two overlap in an overly simplistic way. Second, the analogical reasoning used to convert Bayes’ rule from events to random variables is highly misleading without the relevant quantifiers. Any attempt to render meaningful the traditional Bayesian interpretation of its key elements, by attaching such quantifiers, belies the likelihood principle. These findings have important implications, not only for Bayesian statistics, but also for Bayesian epistemology and inductive logics, more generally.