The Rate of Convergence for Approximate Bayesian Computation

I am very happy to report that after a long struggle we have finally finished (and submitted) a new paper today:

S. Barber, J. Voss and M. Webster: The Rate of Convergence for Approximate Bayesian Computation. Electronic Journal of Statistics, vol. 9, pp. 80–105, 2015.
DOI:10.1214/15-EJS988, arXiv:1311.2038, more…

The paper studies the convergence of ABC estimates to the correct value. In particular,

• we prove that the method converges under very weak conditions,
• we show that the tolerance parameter δ should be chosen proportional to n^-1/4, where n is the number of accepted ABC samples, and
• we determine the speed of convergence under optimal choice of δ.

Hopefully, these results prove useful for others, too.