Search results
Results From The WOW.Com Content Network
Thus, the Fisher information may be seen as the curvature of the support curve (the graph of the log-likelihood). Near the maximum likelihood estimate, low Fisher information therefore indicates that the maximum appears "blunt", that is, the maximum is shallow and there are many nearby values with a similar log-likelihood. Conversely, high ...
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.
The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. [1] [2] [3 ... for example ...
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.
Fisher information, see also scoring algorithm also known as Fisher's scoring, and Minimum Fisher information, 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. [104]
where () is the Fisher information of the sample. Thus e(T) is the minimum possible variance for an unbiased estimator divided by its actual variance. The Cramér–Rao bound can be used to prove that e(T) ≤ 1.
It states that the precision of any unbiased estimator is at most the Fisher information; or (equivalently) the reciprocal of the Fisher information is a lower bound on its variance. An unbiased estimator that achieves this bound is said to be (fully) efficient.
Information is also a function of the model parameters. For example, according to Fisher information theory, the item information supplied in the case of the 1PL for dichotomous response data is simply the probability of a correct response multiplied by the probability of an incorrect response, or,