Inverse probability

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In probability theory, inverse probability is an obsolete term for the probability distribution of an unobserved variable.

Given a probability distribution p(x|θ) for an observable quantity x conditional on an unobserved variable θ, the "inverse probability" is the posterior distribution p(θ|x). The distribution p(x|θ) itself is called the direct probability.

The terms "direct probability" and "inverse probability" were in use until the middle part of the twentieth century, when the terms "likelihood function" and "posterior distribution" became prevalent. See also Bayesian probability and Bayes' theorem.