Multifidelity approximate Bayesian computation (MF-ABC) is a likelihood-free technique for parameter inference that exploits model approximations to significantly increase the speed of ABC algorithms [T. P. Prescott and R. E. Baker, SIAM/ASA J. Uncertain. Quantif., 8 (2020), pp. 114--138]. Previous work has considered MF-ABC only in context rejection sampling, which does not explore space parti...