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a pri·or·i prob·a·bil·i·ty

An a priori probability is a probability that 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 collectively 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, "uninformative priors" or "objective priors" are particular choices of a priori probabilities. 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.

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