Papers on benchmarks of ODE parameter inference


Does someone in this community happen to know of papers that compare the performance of HMC against other MCMC algorithms in the context of performing inference on ODE models? I’ve got a reviewer fixated on that issue.

So far, I’ve only found

Girolami, M. and Calderhead, B. (2011), Riemann manifold Langevin and Hamiltonian Monte Carlo methods

However, 10 years ago Metropolis was faster (time per ESS) than HMC. At least, in this study.



Huh, that is pretty fast, considering it was 10 years ago…

Table 11 claims that for the Fitzhugh–Nagumo model HMC takes ~800 seconds for ~4k ESS using a single chain initialized at the mode, while Metropolis is slightly (~1.3x) and the best method “Simplified MMALA” is much (~7.3x) faster.

With Stan (on my notebook and with priors as here, not sure what the original priors are) I’m roughly 10x as fast as “Simplified MMALA”, including adaptation, but still…

As for the original question, I don’t know of any such paper, but that doesn’t mean anything.

For the sake of review response my best bet would be separate the discussion of sample and ode solver, so that the NUTS benchmark literature can be pitched along with ODE solver benchmark results (say, CVODES).