Score Function

The score function is the partial derivativeof the log-likelihood function , where is the standard likelihood function.

Defining the likelihood function

(1)

shows that

(2)

and thus that

			(3)
			(4)
			(5)

Using the above formulation of , one can easily compute various statistical measurements associated with . For example, the mean can be shown to equal zero while the variance is precisely the Fisher information matrix. The score function has extensive uses in many areas of mathematics, both pure and applied, and is a key component of the field of likelihood theory.