Fisher information

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• Jeffreys Prior

The Fisher information in a univariate model is given by:

\begin{equation} I(\theta)=-\mathrm{E}_{\mathbf{Y} | \theta}\left[\frac{\partial^{2}}{\partial \theta^{2}} \log p(\boldsymbol{y} | \theta)\right] \end{equation}

for data \(\mathbf{Y}\). In a multivariate model, the Fisher information matrix, has \(ij\) entry:

\begin{equation} I_{i j}(\boldsymbol{\theta})=-\mathrm{E}_{\mathbf{Y} | \theta}\left[\frac{\partial^{2}}{\partial \theta_{i} \partial \theta_{j}} \log p(\boldsymbol{y} | \boldsymbol{\theta})\right] \end{equation}