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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“... 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)