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:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)