The probability of an event E conditioned on evidence X is proportional to the prior probability of the event and the likelihood of the evidence given that the event has occurred. This is Bayes' Theorem:
P(X) is the normalizing constant, which is also called the marginal probability of X. P(E) is the prior, and P(X|E) is the likelihood. P(E|X) is also called the posterior probability.
Bayes' Theorem expressed in terms of the posterior and prior odds is known as Bayes' Rule.
Estimating the hidden probability density function of a random variable from sample data randomly drawn from the population is known as density ...