likelihood function

In Bayesian statistics, the likelihood function is the conditional probability of an event representing evidence or an observation, ie., data, given a second event, sometimes called a parameter.

Consider an event and evidence of that event, another event itself, B. The likelihood function is the conditional probability P(B|A).

In contrast, the posterior probability is the conditional probability of the event A given the evidence of the event, B, P(A|B).

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

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

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