Scoring algorithm

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Scoring algorithm, also known as Fisher's scoring,[1] is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher.

Sketch of Derivation[edit]

Let be random variables, independent and identically distributed with twice differentiable p.d.f. , and we wish to calculate the maximum likelihood estimator (M.L.E.) of . First, suppose we have a starting point for our algorithm , and consider a Taylor expansion of the score function, , about :


is the observed information matrix at . Now, setting , using that and rearranging gives us:

We therefore use the algorithm

and under certain regularity conditions, it can be shown that .

Fisher scoring[edit]

In practice, is usually replaced by , the Fisher information, thus giving us the Fisher Scoring Algorithm:


See also[edit]


Jennrich, R. I., & Sampson, P. F. (1976). Newton-Raphson and related algorithms for maximum likelihood variance component estimation. Technometrics, 18, 11-17.