This lesson provides the background material for the method of maximum likelihood. It explains the relationship of *likelihood* to *probability* and when the terms *likelihood* and *likelihood ratio* can be used interchangeably.

Probability is associated with a forward experiment in which the probability model is specified, including values for the parameters in that model (e.g., mean and variance in a Gaussian density function), and data (i.e., realizations) are generated using this model. In likelihood, on the other hand, the data are given, as well as the nature of the probability model; but the parameters of the probability model are not specified. They must be determined from the given data. Likelihood is, therefore, ...

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