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Maximum likelihood estimation is a method of estimating the parameters of an assumed probability distribution, given some observed data.

This is done by maximizing a likelihood function so that, under the assumed statistical model, the observed data is as likely as possible.

The point in parameter space that maximizes the likelihood function is called the maximum likelihood estimate.

Maximum likelihood logic is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

The likelihood function is differentiable and the derivative test to determine the maxima can be applied.

In some cases, the first-order conditions of the likelihood function can be solved explicitly.

The ordinary least squares estimator maximizes the likelihood of the linear regression model.

In most cases, numerical methods will be needed to find the maximum of the likelihood function.