Likelihood Function

In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values. Likelihood functions play a key role in statistical inference, especially methods of estimating a parameter from a set of statistics.

In non-technical parlance, "likelihood" is usually a synonym for "probability." But in statistical usage, a clear technical distinction is made depending on the roles of the outcome or parameter.

  • Use probability when describing a function of the outcome given a fixed parameter value.
    • “Given that I have flipped a coin 100 times and it is a fair coin, what is the probability of it landing heads-up every time?"
  • Use likelihood when describing a function of a parameter given a fixed outcome.
    • "Given that I have flipped a coin 100 times and it has landed heads-up 100 times, what is the likelihood that the coin is fair?"

Read more about Likelihood Function:  Definition, Log-likelihood, Likelihood Function of A Parameterized Model, Example 1, Example 2, Likelihoods That Eliminate Nuisance Parameters, Historical Remarks

Famous quotes containing the words likelihood and/or function:

    What likelihood is there of corrupting a man who has no ambition?
    Samuel Richardson (1689–1761)

    The function of muscle is to pull and not to push, except in the case of the genitals and the tongue.
    Leonardo Da Vinci (1425–1519)