  Approximate Bayesian computation (ABC) is computationally intensive for
complex model simulators. To exploit expensive simulations, data-resampling via
bootstrapping can be employed to obtain many artificial datasets at little
cost. However, when using this approach within ABC, the posterior variance is
inflated, thus resulting in biased posterior inference. Here we use stratified
Monte Carlo to considerably reduce the bias induced by data resampling. We also
show empirically that it is possible to obtain reliable inference using a
larger than usual ABC threshold. Finally, we show that with stratified Monte
Carlo we obtain a less variable ABC likelihood. Ultimately we show how our
approach improves the computational efficiency of the ABC samplers. We
construct several ABC samplers employing our methodology, such as rejection and
importance ABC samplers, and ABC-MCMC samplers. We consider simulation studies
for static (Gaussian, g-and-k distribution, Ising model, astronomical model)
and dynamic models (Lotka-Volterra). We compare against state-of-art sequential
Monte Carlo ABC samplers, synthetic likelihoods, and likelihood-free Bayesian
optimization. For a computationally expensive Lotka-Volterra case study, we
found that our strategy leads to a more than 10-fold computational saving,
compared to a sampler that does not use our novel approach.
