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Maximum Likelihood is a method for estimating parameters for distributions. For example, if you have a set of independent3.4 data points, X, where X is a vector of points that have been collected from the same normal distribution where $ \mu $ and $ \sigma^2$ are unknown, then maximum likelihood would derive $ \hat{\mu}$ and $ \hat{\sigma}^2$, estimates for $ \mu $ and $ \sigma^2$ respectively. The maximum likelihood estimates (MLEs) are such that they maximize the probability or likelihood of the data, X.

Frank Starmer 2004-05-19