likelihoodˈlaɪk liˌhʊd
likelihood (n)
English Definitions:
likelihood, likeliness (noun)
the probability of a specified outcome
likelihood (Noun)
The probability of a specified outcome; the chance of something happening; probability; the state of being probable.
likelihood (Noun)
Shorthand for likelihood function; the probability that a real world experiment would generate a specific datum, as a function of the parameters of a mathematical model.
likelihood (Noun)
Likeness, resemblance.
likelihood (Noun)
Appearance, show, sign, expression.
likelihood
The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood function indicates which parameter values are more likely than others, in the sense that they would have made the observed data more probable. Consequently, the likelihood is often written as L ( θ ∣ X ) {\displaystyle {\mathcal {L}}(\theta \mid X)} instead of P ( X ∣ θ ) {\displaystyle P(X\mid \theta )} , to emphasize that it is to be understood as a function of the parameters θ {\displaystyle \theta } instead of the random variable X {\displaystyle X} . In maximum likelihood estimation, the arg max of the likelihood function serves as a point estimate for θ {\displaystyle \theta } , while the Fisher information (often approximated by the likelihood's Hessian matrix) indicates the estimate's precision. Meanwhile in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' rule.
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