"And despite what the autodiff people say, that might be hard and/or not very useful in practice, if your likelihood is based on running a lengthy astrophysical simulation."
Only if you treat the simulation as an un-interrogatable black box. All of those astro simulations are ODE or PDE systems of one kind or another which can be very cleanly autodiffed to calculate exact gradients. N-bodies are particularly well-suited to this approach.
"You can run HMC on any differentiable surrogate surface surface. It's only the accept/reject step that has to use your real model and data. You might consider that if you have a less hairy approximation to your model."
You _can_ but it won't work above O(10) dimensions. The problem is that the more dimension you have the more any surrogate surface (and its gradients) will drift away from the true surface and worse your acceptance probabilities will be.
With exact gradients the optimal performance of HMC will drop negligibly with dimension (you need to get up O(2^100) or so before you really start to see problems), assuming the target distribution itself doesn't get more complex its dimension increases.
Only if you treat the simulation as an un-interrogatable black box. All of those astro simulations are ODE or PDE systems of one kind or another which can be very cleanly autodiffed to calculate exact gradients. N-bodies are particularly well-suited to this approach.
"You can run HMC on any differentiable surrogate surface surface. It's only the accept/reject step that has to use your real model and data. You might consider that if you have a less hairy approximation to your model."
You _can_ but it won't work above O(10) dimensions. The problem is that the more dimension you have the more any surrogate surface (and its gradients) will drift away from the true surface and worse your acceptance probabilities will be.
With exact gradients the optimal performance of HMC will drop negligibly with dimension (you need to get up O(2^100) or so before you really start to see problems), assuming the target distribution itself doesn't get more complex its dimension increases.