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

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?

• If you can compute the likelihood function at the same cost as for the ABC computation, there is no debate as to which method to use: go for the exact Bayesian solution. – Xi'an Feb 23 '15 at 16:45
• do you have any comments on the Toni paper? Maybe I'm not understanding something, but the distance functions require ODE integration and it seems to me there's not much of a computational savings in using SSE relative to explicitly evaluating the actual likelihood using a gaussian noise model. Why not apply SMC using the full likelihood? – user4733 Feb 23 '15 at 17:12
• – Tim Jun 19 '17 at 12:42