Observed 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.

Suppose we observe random variables ${\displaystyle X_{1},\ldots ,X_{n}}$, independent and identically distributed with density f(X; θ), where θ is a (possibly unknown) vector. Then the log-likelihood of the parameters ${\displaystyle \theta }$ given the data ${\displaystyle X_{1},\ldots ,X_{n}}$ is

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