Fisher information

Alex Reinhart – Updated August 17, 2016 notebooks ·

See Schervish’s Theory of Statistics, sections 2.3.1 and 7.3.5, or Pawitan’s In All Likelihood, chapter 8, for a more intuitive introduction.

Observed vs. expected information

Observed information has the direct interpretation as the negative second derivative (or Hessian) of the log-likelihood, typically evaluated at the MLE. When the MLE is asymptotically normal, the Fisher information is the inverse of its covariance matrix, raising the question of whether we should use observed or expected information.

Use to test identifiability

There is a connection between the Fisher information matrix and identifiability.