Maximum likelihood estimation of models

The method of maximum likelihood (ML) is a standard way of estimating parameters of statistical models. It involves choosing as estimates the parameter values that make the probability of obtaining the observed data (the likelihood function) as large as possible. There are several reasons why this method is favoured by many statisticians. Mainly, it is because under fairly general conditions, with large samples, ML estimators are unbiased, have the smallest possible variance, and have variances and covariances that can be approximated fairly easily. Also, the method provides a systematic way of determining estimates that can be applied purely numerically if necessary. A disadvantage in some cases is that estimates can only be determined after lengthy iterative calculations that may not converge on stable values.