### Fisher information

**(Fisher score)**
(measure of the information provided by experimental data)

**Fisher information** is a measure of the information provided
by a set of experimental data regarding a **probability distribution**
such as a probability mass function (PMF) or probability density function (PDF). In the common case of determining
such a distribution through experiment, Fisher information provides
some measure of the value of a particular experimental design and
can be used to optimize planned experiments.

Given a set (e.g., range) of candidate probability distributions,
one of which is some actual distribution, one of these candidates'
**likelihood** is the probability that it is the actual distribution,
and the term **likelihood distribution** refers to the probability
distribution of those likelihoods. Given some measurements (e.g.,
through testing), the likelihood distribution can be tightened,
i.e., some candidate distributions become more probable and others
less so. *Fisher information* is a calculated value that measures
how much some such data will improve this likelihood, the larger
the number, the more information is gleaned from the experiment.

If the probability distribution is over multiple variables,
Fisher information relating to them can be laid out in matrix form
(a **Fisher information matrix** or **Fisher matrix**). The use of
Fisher information to learn about probability distributions from
experimental data has been referred to as the **Fisher technique** or
**Fisher method**.

(*mathematics,statistics,probability*)
**Further reading:**

https://en.wikipedia.org/wiki/Fisher_information

https://www.statisticshowto.com/fisher-information/

https://people.missouristate.edu/songfengzheng/Teaching/MTH541/Lecture%20notes/Fisher_info.pdf

http://wittman.physics.ucdavis.edu/Fisher-matrix-guide.pdf

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