Fisher Information

${\mathcal{I}}_X(\theta ):=\mathbb{E}[(\frac{\partial }{\partial \theta }\log (f_{\theta }(X){)}^2|\theta ]$ provides us a measure of how much information we can obtain about the model parameters $\theta$ given the observations $X$, where

• $X$ is a Random variable
• $\theta$ is a Vector of scalars
• $f_{\theta }$ is a probability density function for $X$. This function depends on $\theta$.
• $\mathbb{E}$ is the expectation operator

Intuition

Fischer information measures how much information do the observations we made of a random variable $X$ give us about the correct values of the underlying $\theta$.