likelihood

Likelihood function

A likelihood function or just likelihood measures how well a statistical model explains observed data, by calculating the probability of seeing that data under different parameter values:

$$\begin{array}{r}\mathcal{L}(\theta \mid x)=f_{\theta }(x)\end{array}$$

Where $\mathcal{L}:\theta \mapsto f(x\mid \theta )$ is the likelihood function, $\theta$ are the parameters of the model, $x$ is the observed data and $f_{\theta }:x\mapsto f(x\mid \theta )$ is a probability density function or probability mass function, where $x$ is a realization of the random variable $X$.