  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 (Prescott and Baker, 2020).
Previous work has considered MF-ABC only in the context of rejection sampling,
which does not explore parameter space particularly efficiently. In this work,
we integrate the multifidelity approach with the ABC sequential Monte Carlo
(ABC-SMC) algorithm into a new MF-ABC-SMC algorithm. We show that the
improvements generated by each of ABC-SMC and MF-ABC to the efficiency of
generating Monte Carlo samples and estimates from the ABC posterior are
amplified when the two techniques are used together.
