Definition
The score or efficient score is the gradient (the vector of partial derivatives), with respect to some parameter, of the logarithm (commonly the natural logarithm) of the likelihood function. If the observation is and its likelihood is, then the score can be found through the chain rule:
Thus the score indicates the sensitivity of (its derivative normalized by its value). Note that is a function of and the observation, so that, in general, it is not a statistic. However in certain applications, such as the score test, the score is evaluated at a specific value of (such as a null-hypothesis value, or at the maximum likelihood estimate of ), in which case the result is a statistic.
Read more about this topic: Score (statistics)
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