Posterior probability
Also known as: Posterior
Your updated belief about a hypothesis after weighing the evidence.
What it means
A posterior probability is the probability of a hypothesis or parameter after the prior has been updated by the data through Bayes' theorem. It synthesizes what was believed beforehand with what the new evidence implies, and it serves as the prior for any further updating as more data arrive. The full posterior distribution, not just a single number, is the object of Bayesian inference, supporting credible intervals and direct probability statements. Because it depends jointly on the prior and the likelihood, two analysts with different priors can reach different posteriors from the same data — a difference that shrinks as evidence grows.
Examples
After a positive diagnostic test, the posterior probability of disease folds together the test's accuracy and the condition's base rate.
A spam filter starts from the odds that any email is junk, folds in what 'FREE' in the subject line implies, and lands on an updated probability for this message.
A team hopeful about a new checkout design sees three weeks of mildly encouraging data; their updated confidence lands between the hunch and the evidence, and moves again as numbers accumulate.
First described in Bayesian tradition; Bayes (1763), Laplace.