Fisher information

Definition

$I(\theta )=E\left[{\left(\frac{\partial }{\partial \theta }\ln f(\mathbf{X};\theta )\right)}^2\right]$ An alternative (often easier to compute) form for the Fisher Information, assuming certain regularity conditions are met, is:

$$I(\theta )=-E\left[\frac{{\partial }^2}{\partial {\theta }^2}\ln f(\mathbf{X};\theta )\right]$$