In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data. Likelihood functions play a key role in frequentist inference, especially methods of estimating a parameter from a set of statistics. In informal contexts, “likelihood” is often used as a synonym for “probability”. In mathematical statistics, the two terms have different meanings. Probability in this mathematical context describes the plausibility of a random outcome, given a model parameter value, without reference to any observed data. Likelihood describes the plausibility of a model parameter value, given specific observed data.
In Bayesian inference, although one can speak about the likelihood of any proposition or random variable given another random variable: for example the likelihood of a parameter value or of a statistical model (see marginal likelihood), given specified data or other evidence, the likelihood function remains the same entity, with the additional interpretations of (i) a conditional density of the data given the parameter (since it is then a random variable) and (ii) a measure or amount of information brought by the data about the parameter value or even the model. Due to the introduction of a probability structure on the parameter space or on the collection of models, it is a possible occurrence that a parameter value or a statistical model have a large likelihood value for a given specified observed data, and yet have a low probability, or vice versa. This is often the case in medical contexts. Following Bayes’ Rule, the likelihood when seen as a conditional density can be multiplied by the prior probability density of the parameter and then normalized, to give a posterior probability density.
The condition or quality of being probable or likely to occur.
Likelihood, probability or chance of occurrence; plausibility or believability.
The probability of a specified outcome; the chance of something happening; probability; the state or degree of being probable.
“In all likelihood the meeting will be cancelled.”
“The likelihood is that the inflation rate will continue to rise.”
The probability that some fixed outcome was generated by a random distribution with a specific parameter.
“”There is no likelihood between pure light and black darkness, or between righteousness and reprobation.” (Sir W. Raleigh)”
Appearance, show, sign, expression.
“”What of his heart perceive you in his face by any likelihood he showed to-day ?” (Shak)”
the state or fact of something’s being likely; probability
“situations where there is a likelihood of violence”
“young people who can see no likelihood of finding employment”