Statistical probability
Among statisticians, there are three distinct interpretations of probability:- Due to the phenomenon known as Statistical Regularity, relative frequency is universally accepted as a legitimate interpretation of probability. This interpretation is most clearly demonstrated with Games of Chance. Consisistency with this interpretation has provoked some conceptual complexities in Statistical Inference which introductory courses attempt to convey to students. Richard von Mises is one of the better known advocates of this point of view.
- Logical probability is an attempt to extend formal logic with truth values intermediate to the conventional end points of false (zero probability) and true (unit probability). This interpretation has been favored by economists like John Maynard Keynes, Frank Plumpton Ramsey, and B. O. Koopman, physicists such as Edwin Thompson Jaynes and Richard T. Cox. In essence, they advocated use of the concept of expected rational utility to develop an operational definition of the probability of any proposition.
- Personal Probability was championed by Leonard J. Savage and Bruno de Finetti as a way of giving meaning to non-repeatable propositions and subjective evaluations of their probability.
An eclectic school has developed which attempts to defuse the debate by focusing on the axioms of mathematical probability as the criterion as to whether an interpretation is valid and/or valuable.
