The maximum-likelihood method is based on the relatively simple idea that different (statistical) populations generate different samples and that any given sample (i.e., set of data) is more likely to have come from some populations than from others.

To determine , we need to determine a formula for the likelihood function and then maximize that function. Because likelihood is proportional to probability, we need to know the entire joint probability density function of the measurements in order to determine a formula for the likelihood function. This, of course, is much more information about Z( ...

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