posterior probability

In Bayesian statistics, the posterior probability is the conditional probability of an event, sometimes called a parameter, given evidence or an observation of that event, the data.

Consider an event and evidence of that event, another event itself, B. The posterior probability is P(A|B). It is called posterior, because event A actually occurs before event B.

In contrast, the likelihood function is the conditional probability of the evidence or observation, B, given the event A, P(B|A).

The posterior probability and the likelihood function are related through Bayes’ Theorem:

P(A|B) =\displaystyle \frac{P(B|A) P(A)}{P|B}

 

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