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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.

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