Probability, Chance, and The Probability of Chance

摘要

In our day-to-day discourse on uncertainty, words like belief, chance, likelihood, and probability are commonly encountered. Often, these words are used interchange- ably, because they are intended to encapsulate some vaguely articulated notion about the unknowns. The purpose of this paper is to propose framework that is able to show how each of these terms can be made to reject a distinct meaning. To construct this framework, we use a basic scenario upon which caveats are introduced. Each caveat motivates us to bring in one or more of the above labels. The scenario considered here is very basic; it arises in both the biomedical and the industrial contexts, and easily generalizes. This paper is expository and much of what is said here is not new. We require of the reader an appreciation of the calculus of probability. However, in order to make our distinctions transparent, probability has to be interpreted subjectively, not as a relative frequency.