**B**arber, Voss, and Webster recently posted and arXived a paper entitled *The Rate of Convergence for Approximate Bayesian Computation*. The paper is essentially theoretical and establishes the optimal rate of convergence of the MSE—for approximating a posterior moment—at a rate of 2/(q+4), where q is the dimension of the summary statistic, associated with an optimal tolerance in n^{-1/4}. I was first surprised at the role of the dimension of the summary statistic, but rationalised it as being the dimension where the non-parametric estimation takes place. I may have read the paper too quickly as I did not spot any link with earlier convergence results found in the literature: for instance, Blum (2010, JASA) links ABC with standard kernel density non-parametric estimation and find a tolerance (bandwidth) of order n^{-1/q+4} and an MSE of order 2/(q+4) as well. Similarly, Biau et al. (2013, Annales de l’IHP) obtain precise convergence rates for ABC interpreted as a k-nearest-neighbour estimator. And, as already discussed at length on this blog, Fearnhead and Prangle (2012, JRSS Series B) derive rates similar to Blum’s with a tolerance of order n^{-1/q+4} for the regular ABC and of order n^{-1/q+2} for the noisy ABC…