In probability theory, inverse probability is an old term for the probability distribution of an unobserved variable.
Today, the problem of determining an unobserved variable (by whatever method) is called inferential statistics. The method of inverse probability (assigning a probability distribution to an unobserved variable) is called Bayesian probability, the distribution of data given the unobserved variable is the likelihood function (which does not by itself give a probability distribution for the parameter), and the distribution of an unobserved variable, given both data and a prior distribution, is the posterior distribution. The development of the field and terminology from "inverse probability" to "Bayesian probability" is described by Fienberg (2006).
