**A** paper on the comparison of emulation methods for Approximate Bayesian Computation was recently arXived by Jabot et al. The idea is to bypass costly simulations of pseudo-data by running cheaper simulation from a pseudo-model or emulator constructed via a preliminary run of the original and costly model. To borrow from the paper introduction, ABC-Emulation runs as follows:

- design a small number
*n*of parameter values covering the parameter space; - generate
*n*corresponding realisations from the model and store the corresponding summary statistics; - build an emulator (model) based on those n values;
- run ABC using the emulator in lieu of the original model.

A first emulator proposed in the paper is to use local regression, as in Beaumont et al. (2002), except that it goes the reverse way: the regression model predicts a summary statistics given the parameter value. The second and last emulator relies on Gaussian processes, as in Richard Wilkinson‘s as well as Ted Meeds’s and Max Welling‘s recent work [also quoted in the paper]. The comparison of the above emulators is based on an ecological community dynamics model. The results are that the stochastic version is superior to the deterministic one, but overall not very useful when implementing the Beaumont et al. (2002) correction. The paper however does not define what deterministic and what stochastic mean…

“We therefore recommend the use of local regressions instead of Gaussian processes.”

While I find the conclusions of the paper somewhat over-optimistic given the range of the experiment and the limitations of the emulator options (like non-parametric conditional density estimation), it seems to me that this is a direction to be pursued as we need to be able to simulate directly a vector of summary statistics instead of the entire data process, even when considering an approximation to the distribution of those summaries.