# Objective priors for simulator-based models?

I've read a bit about how to derive parametrization-invariant priors for models where we have access to derivatives of the likelihood function and can compute the Fisher Information Matrix: http://www.philipgoyal.org/resources/Papers/Research-Papers/MaxEnt2005.pdf

Is there a good way to derive roughly objective priors for simulator-based models, when we don't have access to derivatives of the likelihood function?

So far I've just been using heavy-tailed priors and hoping for the best, but that doesn't seem like the best approach.

To see the connection, imagine that you've fitted a continuous model $p(x|\theta)$ with maximum likelihood. You'd now like to encode $x$ using $\theta$. A simple way to encode the vector $\theta$ is as an array of floating point numbers with fixed precision. Suppose in doing so you introduce an error of size $\epsilon \sim 2^{-p}$ for each coordinate. Since $\theta$ is a MLE estimate, this will create a second order effect on $p(x|\theta)$ that will depend on the hessian of the likelihood function and $\epsilon^2$. If the function is peaked enough (or a member of the exponential family) this is approximately going to be... the Fisher Information Matrix! Dum dum dum...