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How Likelihood* Works

 

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*Likelihood is the probability of the data.

There are more complicated definitions, like ...

The density function of continuous random variables, definition of X, that depend on model parameters, defintion of theta, and written asf(X, given theta), is the probability density function of X vector, giventheta vector, or is the likelihood of theta vector, given X vector, often written as likelihood of theta, given X.

(Which definition do you prefer?  Me too.)

The statistical literature often uses "likelihood" and "loglikelihood" interchangeably, which can be confusing to the statistical newcomer, but in practice it is rather easy to distinguish the two based on context.

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