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.
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Definition
Suppose we observe random variables
We define the observed information matrix at
In many instances, the observed information is evaluated at the maximum-likelihood estimate.
Fisher information
The Fisher information
Applications
In a notable article, Bradley Efron and David V. Hinkley argued that the observed information should be used in preference to the expected information when employing normal approximations for the distribution of maximum-likelihood estimates.