I have a model with a number of parameters. I can calculate the posterior distribution of the parameter vector. This, in part, means that I can calculate the expected value and the variance of each parameter.

Question. How do I calculate model uncertainty as a single quantity? While I have some ad hoc ideas, I'd like to take a principled approach.

One idea is to look at the variance of the likelihood: $\displaystyle Var( L(\theta) )$ ? I'm not sure how to approach this, other than numerically.

Another idea is to compute something like this:

$\displaystyle \sum_i \left | \frac {\partial L} {\partial \theta_i} \right | \sigma_i $

Any and all help appreciated.