A Deep Connection is Drawn Between ‘Evidential Probability’ Theory and ‘Objective Bayesian Epistemology’

A Deep Connection is Drawn Between ‘Evidential Probability’ Theory and ‘Objective Bayesian Epistemology’: Evidential probability (EP), developed by Henry Kyburg, offers an account of the impact of statistical evidence on single-case probability. According to this theory, observed frequencies of repeatable outcomes determine a probability interval that can be associated with a proposition. After giving a comprehensive introduction to EP in §2, in §3 we describe a recent variant of this approach, second-order evidential probability (2oEP). This variant, introduced in Haenni et al. (2008), interprets a probability interval of EP as bounds on the sharp probability of the corresponding proposition. In turn, this sharp probability can itself be interpreted as the degree to which one ought to believe the proposition in question. At this stage we introduce objective Bayesian epistemology (OBE), a theory of how evidence helps determine appropriate degrees of belief (§4). OBE might be thought of as a rival to the evidential probability approaches. However, we show in §5 that they can be viewed as complimentary: one can use the rules of EP to narrow down the degree to which one should believe a proposition to an interval, and then use the rules of OBE to help determine an appropriate degree of belief from within this interval. Hence bridges can be built between evidential probability and objective Bayesian epistemology.