Likelihood Function

Definition

The Likelihood Function is a very general expression that captures the joint probability of observing a particular statistical sample (under IID assumption) given a particular set of parameters of a parametric statistical moodel

Maximizing the likelihood function (for classes of models where this is tractable) is the standard method of estimating a statistical model's parameters

Formula

$L(\beta | X) = \prod_{i}^{N} \phi(x_i, \beta)$

where

• N is the sample size
• $phi$ is the probability of individual observation given $\beta$

See Also

• wikipedia:Likelihood_function