A priori probability
The term a priori probability is used in distinguishing the ways in which values for probabilities can be obtained. In particular, an "a priori probability" is derived purely by deductive reasoning. One way of deriving a priori probabilities is the principle of indifference, which has the character of saying that, if there are N mutually exclusive and exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/N. Similarly the probability of one of a given collection of K events is K/N.
One disadvantage of defining probabilities in the above way is that it applies only to finite collections of events.
Similar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference a priori denotes knowledge about the prior distribution, while a posteriori denotes knowledge about the posterior distribution.
- Mood A.M., Graybill F.A., Boes D.C. (1974) Introduction to the Theory of Statistics (3rd Edition). McGraw-Hill. Section 2.2 (available online)
- E.g. Harold J. Price and Allison R. Manson, "Uninformative priors for Bayes’ theorem", AIP Conf. Proc. 617, 2001
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