Likelihood function

The likelihood function (often simply called the likelihood) is the joint probability (or probability density) of observed data viewed as a function of the parameters of a statistical model.

In maximum likelihood estimation, the arg max (over the parameter ${\displaystyle \theta }$) of the likelihood function serves as a point estimate for ${\displaystyle \theta }$, while the Fisher information (often approximated by the likelihood's Hessian matrix) indicates the estimate's precision.

In contrast, in Bayesian statistics, parameter estimates are derived from the converse of the likelihood, the so-called posterior probability, which is calculated via Bayes' rule.