posterior distribution

In Bayesian reasoning this is the probability calculated after combining fresh evidence with the prior distribution. It is given by Bayes rule: Posterior(A_f|E) = P(E|A_f)xPrior(A_f)/(Σ_{all i} P(E|A_i)xPrior(A_i)), where E is the evidence, and A_i ranges over all alternatives including the focus one A_f. Note that in Bayesian statistics the posterior distribution is typically not a real probability but a quantified belief or plausibility.