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Encyclopedia > Fisher information metric

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

  Results from FactBites:
 
Fisher information - Wikipedia, the free encyclopedia (673 words)
Fisher information 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 Fisher information 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.
  More results at FactBites »


 

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