# A priori probability

Not to be confused with prior 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.[1] 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.

In Bayesian inference, the terms "uninformative priors" or "objective priors" refer to particular choices of a priori probabilities.[2] Note that "prior probability" is a broader concept.

Similar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference a priori denotes general knowledge about the data distribution before making an inference, while a posteriori denotes knowledge that incorporates the results of making an inference.[3]

## References

1. ^ 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)
2. ^ E.g. Harold J. Price and Allison R. Manson, "Uninformative priors for Bayes’ theorem", AIP Conf. Proc. 617, 2001
3. ^ Eidenberger, Horst (2014), Categorization and Machine Learning: The Modeling of Human Understanding in Computers, Vienna University of Technology, p. 109, ISBN 9783735761903.