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Maximum likelihood estimation starts with the mathematical expression known as a likelihood function of the sample data. This expression contains the unknown parameters to be estimated. Those values of the parameters that maximize the sample likelihood are known as the maximum likelihood estimates which are determined by setting the partial derivative of the likelihood function to zero (i.e. finding the location of the function's peak with respect to the estimated parameters).


Maximum likelihood methods have desirable mathematical and optimality properties: they become minimum minimum variance unbiased estimators as the sample size increases. They often have approximate normal distributions and with a Taylor series expansion calculation they can be used to generate Normal distributions of uncertainty.