Baidu Encyclopedia version
The posterior probability is one of the basic concepts of information theory.
In a communication system, after receiving a certain message, the probability that the message is known by the receiving end is called the posterior probability. The calculation of the posterior probability is based on the prior probability. The posterior probability can be calculated from the Bayesian formula using the prior probability and likelihood function.
In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is that the conditional probability is assigned to the relevant evidence or background consideration. Similarly, the posterior probability distribution is an unknown probability distribution that is treated as a random variable, subject to evidence obtained from experiments or investigations. In this case, “posterior” refers to the relevant evidence after considering the specific case being examined.
For example, if a person digs at a random point, they will find ("non-posterior") probabilities. If they dig in the place where the metal detector sounds, they will find the posterior probability of the buried treasure.