In statistics and information theory, the expected formation matrix of a likelihood function
is the inverse of the observed information matrix of
[1] Currently, no notation for dealing with formation matrices is widely used, but in books and articles by Ole E. Barndorff-Nielsen and Peter McCullagh, the symbol
is used to denote the element of the i-th line and j-th column of the observed formation matrix.
The geometric interpretation of the Fisher information matrix (metric) leads to a notation of
following the notation of the (contravariant) metric tensor in differential geometry.
The Fisher information metric is denoted by
These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio.