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."
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
