Likelihood function

A likelihood function (often simply called the likelihood) gives the relative merit of various statistical models for describing a data set. Often the models being compared are parameterized by a parameter, with the parameter often written as θ, or they are parameterized by multiple parameters given as the components of a vector. For a probability function (or probability density function) Pr[x | θ] that gives the probability (or probability density) of data x for a given model-specifying parameter θ, the likelihood is any function of θ equal to cPr[x | θ] for some positive value c.

In contrast, in Bayesian statistics, the estimate of interest is the converse of the likelihood, the so-called posterior probability of the parameter given the observed data, which is calculated via Bayes' rule.