# what is the easy way to estimate expected Fisher information matrix for a given functional model?

Hi guys I am doing some model selection and need to estmiate both observed and expected Fisher Information Matrix to calculate this link. How do you estimate that expected one numerically?

I find it easiest to understand these things if I first consider a model with a single parameter, call it $\theta$. Typically we want to choose $\theta$ so as to maximize the likelihood (i.e. conditional probability) of the data we observe. Actually, it's more useful to maximize the log of the likelihood, so that rather than multiplying the likelihoods of all the observed data, we just add their logs. It's just a process of hill-climbing.
The top of that hill (log-likelihood as a function of $\theta$) has a sharpness, or curvature, which is its second derivative, and it's negative. You can calculate this numerically by moving $\theta$ around. The sharper it is, the more informative $\theta$ is.
Then all you have to do is extend $\theta$ to a vector, in which the second derivative becomes a matrix, the Fisher Information Matrix (FIM). If you maximize its determinant, that's called D-optimality.