Observed information
In statistics, the observed information, or observed Fisher information, is the negative of the second derivative of the "log-likelihood". It is a sample-based version of the Fisher information.Definition
Suppose we observe random variables, independent and identically distributed with density f, where θ is a vector. Then the log-likelihood of the parameters given the data is
We define the observed information matrix at as
In many instances, the observed information is evaluated at the maximum-likelihood estimate.Fisher information
The Fisher information is the expected value of the observed information given a single observation distributed according to the hypothetical model with parameter :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.
