Evidential Probability

We characterize and illustrate evidential probability — an interval-valued measure of uncertainty that applies to sentences. Evidential probability is also taken to be relative to a body of knowledge or a database representing the data on which judgments of uncertainty are to be made. Every statement is equivalent to some statement to which statistics in the database are relevant. The problem is to find the correct statement; this is the problem of finding the correct reference class for a statement. A set of rules for determining the correct reference class is offered. 1 Kinds of Probability Most scientists feel most comfortable with some kind of frequency or empirical interpretation of probability [Wilson, 19521. It is not merely that this way of looking at probability seems to have a comfortable history in casinos, but that it is what physicists employ in their theoretical work in quantum mechanics as well as in statistical mechanics. It is also what is natural to have in mind in dealing with "random er-ror" in measurement. Indeed, it is the basic idea that is called on when we need to go from the "random er-rors" in a number of individual measurements of different quantities, to the "inferred error" in a quantity that is taken as a function of those measured quantities. This is a relatively uncontroversial framework for "combining" probabilities. In designing expert systems, however, what we have to work with are often the mere opinions of experts. It is said that "we have no statistics." (McCarthy and Hayes, 1969) Every event that we need to concern ourselves with, after all, is "unique." (That's the nature of events!) And there is a well developed interpretation of probability as subjective: the view developed by L. This approach to probability has been widely adopted in business schools, and is accepted by a significant minority of statisticians [Raiffa and Schlaifer, 1961]. Prima facie, the problem with subjective t is subjective; the founding fathers just cited make crystal clear that that is exactly what they intended: one man's coherent opinion is, formally, as good as another's. Ramsey was self-consciously clear about this: "Ia man's] original expectations may within the limits of consistency be any he likes..." (p. 189) In contrast to both of these views, evidential probability both applies to unique events, and is solidly based on statistical evidence. This is not a new interpretation; it is a philosophical interpretation that …