# Numerical calculation of fisher information

I am trying to obtain numerically the fisher information. Given a likelihood function $$f(X,\theta),$$ with $X \in [0,1]$. The fisher information is given by $$\mathbb{I}(\theta)=\mathbb{E}\left[\left. \frac{\partial^2 \text{log }f( X|\theta)}{\partial \theta^2}\right|_{\theta=\theta^*} \right].$$

To calculate this numerically in Matlab is use this formula: $$\mathbb{I}(\theta) = \int_0^1 \frac{\partial^2 \text{log }f( X|\theta)}{\partial \theta^2} \cdot f(X,\theta) \quad dX$$

Am I doing this correct?

• @Learner Yes ,it is. I corrected my question. Commented Mar 20, 2013 at 12:44
• There is a negative sign missing and $\theta^\star$ should be equal to $\theta$. Commented Mar 20, 2013 at 12:52
• @Learner, thanks a lot. Commented Mar 20, 2013 at 12:57
• What's the distribution of X? i.e. what is the functional form of f(x)? Since most Fisher Information problems are defined in terms of the parameters, you may find that you need symbolic methods, not numerical ones. Commented Apr 26, 2013 at 14:38

The formula i've always used is, $$\mathbb{I}_{ij}(\theta) = \int\limits_\mathbb{R} f(x,\theta) \frac{\partial \ln f(x,\theta)}{\partial \theta_{i}} \frac{\partial ln \ f(x,\theta)}{\partial \theta_{j}} dx$$