How is ABC more computationally efficient than exact Bayesian Computation for parameter estimation in dynamical systems (ODE) models?

Question

Approximate Bayesian Computation has been suggested as an approach to parameter estimation for computationally intensive simulations, most commonly in population genetics, but also in dynamical systems, for example, Toni 2009 and applied in the corresponding abc-sysbio tool pubished in nat methods.

In a dynamical systems model, the likelihood is expensive to calculate because it requires running a simulation to evaluate the likelihood. However, unlike stochastic population genetics model, one could reasonably obtain a likelihood from a dynamical systems model by imagining a probabilistic representation of the RMSE (e.g. treating errors as normally distributed) and obtain a likelihood from a single simulation.

So in both exact and approximate bayesian computation, each likelihood calculation entails running a single ODE simulation, how is it that ABC is computationally advantageous as compared to exact bayesian computation approaches? Where does the speedup come from?

Answer 1

It looks like it is similar to HMC in that it uses a type of stochastic gradient instead of a random walk. I didn't see anywhere that they say they could do the estimate based on a single simulation. Instead, it looks like you can simply get good values much faster. It really looks very similar to HMC as it's implemented in Stan. I would actually recommend Stan, since it looks like it has better documentation and there are some books on it currently.