Prior probabilityRefers to the probability obtained based on past experience and analysis, usually statistical probability. In Bayesian statistics, the prior probability distribution refers to the probability distribution of the variable P, which is a probability prediction of the uncertainty of P before obtaining certain information or evidence.

Prior Probability and Posterior Probability

• Prior probability: represents the estimated probability of a parameter under certain data, i.e. P(A);
• Maximum likelihood: find a parameter that maximizes the probability of the observable data occurring, that is, P(A | B)/P(B);
• Posterior probability: the maximum probability value that occurs under maximum likelihood conditions, that is, P(A | B).

P(A | B) is the conditional probability of A given that B occurs. Since we know the value of B, it is called the posterior probability of A.

P(A) is the prior probability of A, which does not take into account any factors of B;

P( B | A ) is the conditional probability of B given that A has occurred. Since we know the value of A, it is called the posterior probability of B.

P(B) is the prior probability of B without considering any factors related to A.

Synonym: posterior probability