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The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys ...
In information geometry, the Fisher information metric [1] is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability distributions. It can be used to calculate the distance between probability distributions. [2] The metric is interesting in several aspects.
In information theory, the principle of minimum Fisher information (MFI) is a variational principle which, when applied with the proper constraints needed to reproduce empirically known expectation values, determines the best probability distribution that characterizes the system. (See also Fisher information.)
In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function). It is a sample-based version of the Fisher information.
The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. [1] [2] [3] [4] [5] It is ...
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Fisher has also been praised as a pioneer of the Information Age. [29] His work on a mathematical theory of information ran parallel to the work of Claude Shannon and Norbert Wiener, though based on statistical theory. [30] [31] A concept to have come out of his work is that of Fisher information. [32]
It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric [3] when restricted to the pure states alone. Definition [ edit ]