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"For random variable X, with a likelihood function <math>L(θ,X)</math> and score function(with respect to parameter θ) <math>s(θ;X) = \nabla [ln(L(θ,X))]</math>(Rothman)<br /> | "For random variable X, with a likelihood function <math>L(θ,X)</math> and score function(with respect to parameter θ) <math>s(θ;X) = \nabla [ln(L(θ,X))]</math>(Rothman)<br /> | ||
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In more understandable terms this just means that for some probability density function, the amount of information stored in the parameter θ, or Fischer information <math>I(θ)</math> is equal to the variance of the score. | In more understandable terms this just means that for some probability density function, the amount of information stored in the parameter θ, or Fischer information <math>I(θ)</math> is equal to the variance of the score. | ||
Revision as of 19:36, 6 December 2020
The formal definition of Fischer Information is:
"For random variable X, with a likelihood function $ L(θ,X) $ and score function(with respect to parameter θ) $ s(θ;X) = \nabla [ln(L(θ,X))] $(Rothman)
In more understandable terms this just means that for some probability density function, the amount of information stored in the parameter θ, or Fischer information $ I(θ) $ is equal to the variance of the score.
