Which can be thought of intuitively as: "The distance between two points on a statistical differential manifold is the amount of information between them, i.e. the informational difference between them."
Shun'ichi Amari - Differential-geometrical methods in statistics, Lecture notes in statistics, Springer-Verlag, Berlin, 1985
Shun'ichi Amari, Hiroshi Nagaoka - Methods of information geometry, Transactions of mathematical monographs; v. 191, American Mathematical Society, 2000
Fisherinformation is thought of as the amount of information that an observable random variable carries about an unobservable parameter θ upon which the probability distribution of X depends.
The Fisherinformation is thus the expectation of the square of the score.
Information may thus be seen to be a measure of the "sharpness" of the support curve near the maximum likelihood estimate of θ.
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