Fisher information metric Guide, Meaning , Facts, Information and Description
In
mathematics, in
information geometry, the
Fisher information metric is a
metric tensor for a statistical
differential manifold. It can be used to calculate the informational difference between measurements. It takes the form:
Substituting
i = − ln(
p) from
information theory, the formula becomes:
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."
An equivalent form of the above equation is:
See also Cramér-Rao inequality;,
Fisher information
References
- 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
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