In mathematical statistics and information theory, the Fisher information (sometimes simply called information) can be defined as the variance of the score, or as the expected value of the observed information. In Bayesian statistics, the asymptotic distribution of the posterior mode depends on the Fisher information and not on the prior (according to the Bernstein–von Mises theorem, which was anticipated by Laplace for exponential families). The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician R.A. Fisher (following some initial results by F. Y. Edgeworth). The Fisher information is also used in the calculation of the Jeffreys prior, which is used in Bayesian statistics.
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.
Read more about Fisher Information: History, Definition, Matrix Form, Distinction From The Hessian of The Entropy
Famous quotes containing the words fisher and/or information:
“One ... aspect of the case for World War II is that while it was still a shooting affair it taught us survivors a great deal about daily living which is valuable to us now that it is, ethically at least, a question of cold weapons and hot words.”
—M.F.K. Fisher (1908–1992)
“I have all my life been on my guard against the information conveyed by the sense of hearing—it being one of my earliest observations, the universal inclination of humankind is to be led by the ears, and I am sometimes apt to imagine that they are given to men as they are to pitchers, purposely that they may be carried about by them.”
—Mary Wortley, Lady Montagu (1689–1762)