Definition
The posterior probability is the probability of the parameters given the evidence : .
It contrasts with the likelihood function, which is the probability of the evidence given the parameters: .
The two are related as follows:
Let us have a prior belief that the probability distribution function is and observations with the likelihood, then the posterior probability is defined as
The posterior probability can be written in the memorable form as
- .
Read more about this topic: Posterior Probability
Famous quotes containing the word definition:
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)