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 ...

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